Patent ID: 12207481

An artisan of ordinary skill in the art need not view, within isolated figure(s), the near infinite number of distinct permutations of features described in the following detailed description to facilitate an understanding of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The present disclosure is not to be limited to that described herein. Mechanical, electrical, chemical, procedural, and/or other changes can be made without departing from the spirit and scope of the present invention. No features shown or described are essential to permit basic operation of the present invention unless otherwise indicated.

Referring now toFIG.1, the ballistic exciton transistor100comprises an exciton transmission line102comprised of a row of molecules br. The row of molecules brare labeled such because r represents the position of different molecules along the exciton transmission line102, with 0 being an origin defined by the position of the molecule b0proximal to the gate mechanism a. Propagation (delocalization) of excitons along the transmission line102is mediated by exciton exchange interaction(s)104.

The exciton exchange interaction104is represented inFIG.1by at least one solid line between a plurality of the molecules br. The exciton exchange interaction104has a strength characterized by the parameter J. As shown, the gate106comprises a gate molecule a (double circle) that interacts with molecule b0via a two-body exciton interaction108of a strength characterized by the parameter K. If gate molecule a is not excited, the gate molecule a does not couple to the transmission line102. This allows incoming signals110to propagate unimpeded. If gate molecule a is excited, some of the incoming signals110become reflected signals112and are back scattered as a result of the two-body interaction between the exciton residing on gate molecule a and the excitons on the transmission line102.

In one embodiment, the ballistic exciton transistor100can be described as including an excitonic interchange. Like road traffic interchanges, the excitonic interchange can act as a sophisticated junction or junction-like system where exchange interactions can occur. In other words, the excitonic exchange can be thought of as the means by which excitons can be exchanged and otherwise transmitted amongst molecules. For example, the excitonic exchange can comprise a first location at which a linear exciton exchange interaction can occur, said linear exciton exchange interaction being mediated by a transition dipole along the exciton transmission line; and a second location at which a two-body exciton interaction can occur, said two-body exciton being mediated by a difference static dipole along the transmission line.

The ballistic exciton transistor100relies on the exciton exchange interaction104and the two-body exciton interaction108. In the dipole approximation the exciton exchange interaction is mediated by transition dipoles (μ), whereas the two-body exciton interaction is mediated by the difference static dipoles (Δd). The direction of the transition dipole and the difference dipole need not be parallel, as they depend on the molecular structure in different ways. This allows for the possibility of orienting two chromophores (dyes a and b0) such that they can interact only via the two-body exciton interaction.

Squaraine dyes are an example of this in which a pair of two squaraines can be arranged such that their transition dipoles are orthogonal and, hence, do not couple (i.e., propagate an exciton), whereas the exciton-exciton interaction is mediated by a Coulombic quadrupole-quadruple interaction. The asymmetric dyes offered by Dyomics whose product numbers are in the range DY-610 through DY-780 offer examples of this. Molecule a ofFIG.1can be selectively chosen and/or arranged to have such an orientation in relation to the molecules of the transmission line102. Consequently, if molecule a is excited, for example, by the absorption of a photon, the exciton is trapped on the molecule and is able to backscatter excitons propagating on the transmission line. This provides a signal gain in the sense that a single exciton can control the flow of a large number of excitons on the transmission line102.

The Hamiltonian

The molecule labels a and brofFIG.1can also be used to denote the exciton annihilation operator for excitons residing on the molecule. When a single exciton resides on the transmission line102, a single exciton may or may not reside on the gate molecule a. As a consequence, the only two-exciton interaction (e.g.,108) that needs be considered is that between molecule a and the transmission line102. The nearest-neighbor approximation can be made. The transmission line102will be taken to have infinite extent on both sides of b0.

The Hamiltonian operator for the system ofFIG.1can be described as:

H=ℏωo⁢a†⁢a+ℏωK⁢a†⁢b0†⁢b0⁢a+∑r=-∞∞⁢⁢ℏωo⁢br†⁢br+∑r=-∞∞⁢⁢ℏωJ⁡(br+1†⁢br+br†⁢br+1)
where ℏ is a time-dependent constant, ω is a frequency, and † is used to identify specific number operators.
Heisenberg Equations of Motion

The Heisenberg equation of motion for an operator O is

dOdt=iℏ⁡[H,O]+∂O∂t.
The following are equations of motion for the gate molecule a, the proximal molecule b0, and any molecule bralong the transmission line102:

dadt=-i⁢⁢ωo⁢a-i⁢⁢ωK⁢b0†⁢b0⁢a,⁢db0dt=-i⁢⁢ωo⁢b0-i⁢⁢ωK⁢a†⁢ab0-i⁢⁢ωJ⁡(b1+b-1),
and where r≠0,

dbrdt=-i⁢⁢ωo⁢br-i⁢⁢ωJ⁡(br+1+br-1).

Solving for the above Heisenberg equation of motion with the equations of motion for the gate molecule a, the proximal molecule b0, and any molecule bralong the transmission line102yields:

ddt⁢(a†⁢a)=0.

The number operator a†a for the number of excitons on molecule a can be treated as a constant.

Exciton Transmission Lines

If there is no exciton on molecule a, then the number operator a†a can be replaced by its eigenvalue which is zero. In this case, the equation for motion with respect to brholds even at r≠0:

d⁢brd⁢t=-i⁢ωo⁢br-i⁢ωJ⁡(br+1+br-1)
for all r. Due to the translation symmetry the solutions of the above equation of motion will have the Bloch form:

br=12⁢π⁢∫-ππ⁢d⁢k⁢e-i⁡(ωk⁢t-k⁢r)⁢b⁡(k)
where k is the wave number, yielding the dispersion relation:
ωk=ωo+2ωjcos(k).

The group velocity is defined:

vg=∂ωk∂k=-2⁢ωJ⁢sin⁡(k).

Note ωjcan be positive or negative. It is positive if the molecules are aligned side by side (H configuration) or end to end (J configuration). The phase velocity νϕ=ωk/k can have a different speed and sign from that of the group velocity, νg. Note also that the group velocity, νg, has the greatest magnitude when k=±π/2, for which the Bloch form can be written in the form:

br=12⁢π⁢∫0π⁢d⁢k⁢e-i⁡(ωk⁢t-k⁢r)⁢b⁡(k)+12⁢π⁢∫0π⁢d⁢k⁢e-i⁡(ωk⁢t+k⁢r)⁢b⁡(-k)
where the signals carried by b(k) and b(−k) propagate in opposite directions. The transmission line signals110,114propagate unimpeded along the transmission line102.
Exciton Scattering Off of an Exciton

Where ωJis negative, the signals carried by b(k) propagate to the left in the exciton transmission line102shown inFIG.1and those carried by b(−k) propagate to the right. When the numerical operator a†a is not zero, one must solve for the two distinct equations of motion provided above (i.e., solve for when r≠0 and when r=0).

For r≠0, the result is still:

br=12⁢π⁢∫0π⁢d⁢k⁢e-i⁡(ωk⁢t-k⁢r)⁢b⁡(k)+12⁢π⁢∫0π⁢d⁢k⁢e-i⁡(ωk⁢t+k⁢r)⁢b⁡(-k)
because causality signals propagating in from infinity will not be influenced by what happens at r=0 until the signals arrive at that point. For signals coming toward r=0 and which are leaving r=0, for the transmission line to the left of r=0, the result is:

br=12⁢π⁢∫0π⁢d⁢k⁢e-i⁡(ωk⁢t-k⁢r)⁢bLo⁢u⁢t⁡(k)+12⁢π⁢∫0π⁢d⁢k⁢e-i⁡(ωk⁢t+k⁢r)⁢bLi⁢n⁡(k)
for r<0 and for the transmission line102to the right of r=0 results in:

br=12⁢π⁢∫0π⁢d⁢k⁢e-i⁡(ωk⁢t-k⁢r)⁢bRi⁢n⁡(k)+12⁢π⁢∫0π⁢d⁢k⁢e-i⁡(ωk⁢t+k⁢r)⁢bRo⁢u⁢t⁡(k)
for r>0.

If the number of excitons at the gate molecule a is zero, variables in the previous two equations can be solved for as follows:
bLout(k)=bRin(k)=b(k)
and
bRout(k)=bLin(k)=b(−k)

If the gate molecule a is excited, then:

b0=12⁢π⁢∫0π⁢d⁢k⁢e-i⁢ωk⁢t⁢b⁡(k)
yielding the following by way of the brequations for r<0 and r>0 above:
(ωk−ωo−ωKa†a)b(k)=ωj[eikbRin(k)+e−ikbRout(k)+e−ikbLout(k)+eikbLin(k)],
ωJb(k)=(ωk−ωo−ωJeik)eikbRin(k)+(ωk−ωwo−ωJe−ik)e−ikbRout(k),
ωJb(k)=(ωk−ωo−ωJe−ik)e−ikbLout(k)+(ωk−ωo−wJeik)eikbLin(k).
Note:
ωk−ωo=ωJ(eik+e−ik)
and thus collectively this yields:
[ωJ(eik+e−ik)−ωKa†a]b(k)=[eikbRin(k)+e−ikbRout(k)+e−ikbLout(k)+eik+bLin(k)]
b(k)=bRin(k)+bRout(k),
b(k)=bLin(k)+bLout(k).
[ωJ(eik+e−ik)−ωKa†a][bRin(k)+bRout(k)]=ωJ[eikbRin(k)+e−ikbRout(k)+e−ikbLout(k)+eik+bLin(k)],
[ωJ(eik+e−ik)−ωKa†a][bLin(k)+bLout(k)]=ωJ[eikbRin(k)+e−ikbRout(k)+e−ikbLout(k)+eik+bLin(k)].

The last two equations rearranged yield:
ωJe−ikbLout(k)−(ωJeik−ωKa†a)bRout(k)=−ωJeikbLin(k)+(ωJe−ik−ωKa†a)bRin(k),
−(ωJeik−ωKa†a)bLout(k)+ωJe−ikbRout(k)=(ωJe−ik−ωKa†a)bLin(k)−ωjeikbRin(k).
This can be reduced by introducing the quantities:
F1=−ωJeikbLin(k)+(ωJe−ik−ωKa†a)bRin(k),
F2=(ωJe−ik−ωKa†a)bLin(k)−ωJeikbRin(k).

Further rewritten, these equations can be expressed as:
ωJe−ikbLout(k)−(ωJeik−ωKa†a)bRout(k)=F1
−(ωJeik−ωKa†a)bLout(k)+ωJe−ikbRout(k)=F2
and in Matrix form:

[ωJ⁢e-i⁢k-(ωJ⁢ei⁢k-ωK⁢a†⁢a)-(ωJ⁢ei⁢k-ωK⁢a†⁢a)ωJ⁢e-i⁢k]⁡[bLo⁢u⁢t⁡(k)bRo⁢u⁢t⁡(k)]=[F1F2].

Solving for bLout(k) and bRout(k), this finds:

bLo⁢u⁢t⁡(k)=ωJ⁢e-i⁢k⁢F1+(ωJ⁢ei⁢k-ωK⁢a†⁢a)⁢F2ωJ2⁢e-i⁢2⁢k-(ωJ⁢ei⁢k-ωK⁢a†⁢a)2andbRo⁢u⁢t⁡(k)=(ωJ⁢ei⁢k-ωK⁢a†⁢a)⁢F1+ωJ⁢e-i⁢k⁢F2ωJ2⁢e-i⁢2⁢k-(ωJ⁢ei⁢k-ωK⁢a†⁢a)2.

In other words:

ωJ⁢e-i⁢k⁢F1+(ωJ⁢ei⁢k-ωK⁢a†⁢a)⁢F2=(ωJ⁢ei⁢k-ωK⁢a†⁢a2-ωJ2)⁢bLi⁢n⁡(k)-2⁢i⁢ωJ⁡[ωJ⁢sin⁡(2⁢k)-ωK⁢sin⁡(k)⁢a†⁢a]⁢bRi⁢n⁡(k),

(ωJ⁢ei⁢k-ωK⁢a†⁢a)⁢F1+ωJ⁢e-i⁢k⁢F2=-2⁢i⁢ωJ⁡[ωJ⁢sin⁡(2⁢k)-ωK⁢sin⁡(k)⁢a†⁢a]⁢bLi⁢n⁡(k)+(ωJ⁢ei⁢k-ωK⁢a†⁢a2-ωJ2)⁢bRi⁢n⁡(k).

One now has:
|ωJeik−ωKa†a|2−ωJ2=−2ωJωKcos(k)a†a+ωK2a†aa†a.

And again, solving for bLout(k) and bRout(k):

bLo⁢u⁢t⁡(k)=ωJ⁢ei⁢k-ωK⁢a†⁢a2-ωJ2ωJ2⁢e-i⁢2⁢k-(ωJ⁢ei⁢k-ωK⁢a†⁢a)2⁢bLi⁢n⁡(k)-2⁢i⁢ωJ⁡[ωJ⁢sin⁡(2⁢k)-ωK⁢sin⁡(k)⁢a†⁢a]ωJ2⁢e-i⁢2⁢k-(ωJ⁢ei⁢k-ωK⁢a†⁢a)2⁢bRi⁢n⁡(k)bRo⁢u⁢t⁡(k)=-2⁢i⁢ωJ⁡[ωJ⁢sin⁡(2⁢k)-ωK⁢sin⁡(k)⁢a†⁢a]ωJ2⁢e-i⁢2⁢k-(ωJ⁢ei⁢k-ωK⁢a†⁢a)2⁢bLi⁢n⁡(k)+ωJ⁢ei⁢k-ωK⁢a†⁢a2-ωJ2ωJ2⁢e-i⁢2⁢k-(ωJ⁢ei⁢k-ωK⁢a†⁢a)2⁢bRi⁢n⁡(k).

The transmission T and the reflection R amplitudes can be introduced as:

T=-2⁢i⁢ωJ⁡[ωJ⁢sin⁡(2⁢k)-ωK⁢sin⁡(k)⁢a†⁢a]ωJ2⁢e-i⁢2⁢k-(ωJ⁢ei⁢k-ωK⁢a†⁢a)2andR=ωJ⁢ei⁢k-ωK⁢a†⁢a2-ωJ2ωJ2⁢e-i⁢2⁢k-(ωJ⁢ei⁢k-ωK⁢a†⁢a)2.

When there are no excitons in molecule a, the number operator a†a can be replaced by zero and one obtains T=1 and R=0. Now:
ωJ2e−i2k−(ωJeik−ωKa†a)2=−2iωJ[ωJsin(2k)−ωKsin(k)a†a]+2ωJωKcos(k)a†a−ωK2a†aa†a.

The transmission amplitude can be rewritten as:

T=2⁢i⁢ωJ⁡[ωJ⁢sin⁡(2⁢k)-ωK⁢sin⁡(k)⁢a†⁢a]2⁢i⁢ωJ⁡[ωJ⁢sin⁡(2⁢k)-ωK⁢sin⁡(k)⁢a†⁢a]+2⁢ωJ⁢ωK⁢cos⁡(k)⁢a†⁢a-ωK2⁢a†⁢aa†⁢a.

The transmission coefficient (transmission probability) can be expressed:

T2=4⁢ωJ2⁡[ωJ⁢⁢sin⁡(2⁢k)-ωK⁢sin⁡(k)⁢a†⁢a]24⁢ωJ2⁡[ωJ⁢sin⁡(2⁢k)-ωK⁢sin⁡(k)⁢a†⁢a]+[2⁢ωJ⁢ωK⁢cos⁡(k)-ωK2⁢a†⁢a]2⁢(a†⁢a)2.

So if one exciton is present in molecule a, a†a can be replaced by 1 and the transmission coefficient can then be expressed as:

T2=4⁢ωJ2⁡[ωJ⁢sin⁡(2⁢k)-ωK⁢sin⁡(k)]24⁢ωJ2⁡[ωJ⁢sin⁡(2⁢k)-ωK⁢sin⁡(k)]+[2⁢ωJ⁢ωK⁢cos⁡(k)-ωK2]2.

The behavior of this system when the excitons are at the bottom of the band can be particularly beneficial because in the case when ωjis negative and k is near zero, a Taylor expansion of trigonometric functions in the equation above will yield:

cos⁢⁢θ=1-θ22!+θ44!+…sin⁢⁢θ=θ-θ33!+θ55!+…

For strong switching, the numerator would ideally be as small as possible. For example, if one were to minimize |wJsin(2k)−ωKsin(k)|, the Taylor expansions would become:

ωJ⁢sin⁡(2⁢k)-ωK⁢sin⁡(k)=(2⁢ωJ-ωK)⁢k-8⁢ωJ-ωK3!⁢k3+…2⁢ωJ⁢cos⁡(k)-ωK=2⁢ωJ-ωK-2⁢ωJ(k22!-k44!+…).

To make the first equation above as small as possible as k approaches 0, the linear order term can be eliminated by setting the condition:
ωK=2ωJ
and with this condition the lowest order becomes:
|T|2=k2.
Midband Performance

For a signal propagating at mid band, that is k=π/2, the condition set above should not be imposed. In this case one has:

T2=4⁢ωJ24⁢ωJ2+ωK2.

To make the transition coefficient as small as possible, one would like to make ωK(that is K) as large as possible. If we choose such a value to satisfy ωK=2ωJthen |T|2=½. Hence, it may be possible to achieve a switching amplitude at room temperature of a factor of at least 2. The equation ωK=2ωJsuggests much higher switching ratios could be achieved at low temperatures.

Bound States

If the two-exciton interaction108, K=ℏωK, is sufficiently strong and negative, exciton-exciton bound states can form between the exciton in the gate molecule a and an exciton on the transmission line102. It is possible to determine the conditions when a bound state can form. It is noted that the existence of such bound states enables other mode of operation of the exciton transistor100. The bound state will suppress the row of excitons102through the transistor100if there is a repulsive two-body interaction108between excitons on the transmission line102. The Hamiltonian for such an interaction would have the form:

He⁢x-e⁢x=∑r=-∞∞⁢KT⁢br+1†⁢br†⁢br⁢br+1
where KTis the interaction energy between two excitons residing on neighboring sites. Alternatively, if the anharmonicity parameter Δ is positive, it will be unfavorable for two excitons to occupy the same molecule and this will suppress the row of excitons102through the exciton transistor100. The Hamiltonian for this interaction is given by:

Han=∑r=-∞∞⁢Δ2⁢br†⁢br†⁢br⁢br.

In the limit Δ→∞ the excitons behave as hard-core Bosons. In this case, flow through the transistor100would be completely suppressed. In this limit, the Hamiltonian can be dispensed with if the molecules brare treated as satisfying Paulion commutation relations. The bound state mode is expected to have the form:
br=bBe−iwκte−κ|r|
where molecules brneed no longer satisfy the usual boson commutation relations. The equations of motion will still need to be satisfied such that:
ωκ−ωo−ωKa†a=2ωJe−κ
and
ωκ=ωo+2ωJcosh(κ).

The two equations together yield:

sinh⁢(κ)=ωK2⁢ωJ⁢a†⁢a
and from this one can obtain:

cosh⁡(κ)=1+(ωK2⁢ωJ⁢a†⁢a)2.

Hence:

ωκ=ωo+2⁢ωJ⁢1+(ωK2⁢ωJ⁢a†⁢a)2.

ωJis negative at the bottom of the transmission line band when k=0. It follows that the energy at the bottom of the band in frequency units is:
ω0=ωo+2ωJ.

The condition for the existence of a bound state is
ωκ<ωo
and with this condition the equations of [0064] and [0065] yield:

ωJ⁢1+(ωK2⁢ωJ⁢a†⁢a)2<ωJ.
and since ωJis negative this further yields:

1+(ωK2⁢ωJ⁢a†⁢a)2>1.
which is satisfied when the numerical operator a†a has an eigenvalue greater than 0. It can be concluded that when ωJis negative and the exciton-exciton interaction is attractive (ωKis negative) there can be a bound state.

The analysis with ωJ<0 and ωK<0 can be plagued by the existence of a bound state unless a proper analysis of transmission through the exciton transistor100is done and one takes into account the bound state.

Suppression of Transmission by a Repulsive Interaction

When ωJ=0 so that the bottom of the band occurs at k=0 and the exciton-exciton interaction is positive ωK>0, suppression of transmission still occurs due to the repulsive interaction. For example, as shown inFIG.2, the transmission probability (coefficient) |T|2is plotted as a function of k for various values of −ωK/ωJ=−K/J. The transmission coefficient peaks at midband k=π/2 where the transmission coefficient reduces to:

T2=4⁢ωJ24⁢ωJ2+ωK2.

Switching on-off contrast improves the larger the ratio |ωK|/|ωJ| becomes. When |ωK|=2|ωJ| this yields |T|2=½. The switching contrast is larger for smaller values of k, that is, when the incoming signals110are near the band minimum. When ωK>>2|ωJ|, the transmission coefficient becomes:

T2=4⁢ωJ2⁢sin2⁡(k)ωK2=4⁢(ωJωK)2⁢sin2⁡(k).

When k<<1, the transmission coefficient becomes:

T2=4⁢(ωJωK)2⁢k2.

For ballistic transport of excitons along a chain of chromophores (e.g., molecules br,), |ωJ| should be as large as possible to minimize decoherence due to exciton-vibron coupling. The exciton transistor described here should then become feasible provided such molecules can be found for which |ωK| is correspondingly large even when the molecular pair is configured such that the transition dipoles are orthogonal.

Constructing an Exciton Transistor

According to one embodiment, the exciton transistor100can be fabricated as shown inFIGS.3-6.

The exciton transistor100can form the heart of an optical switch300shown inFIGS.3-4that can be employed in integrated and fiber optic communications systems. Similarly, the exciton transistor100could also be configured as an optical modulator that can be employed in integrated and fiber optic communications systems. As an analogy can be made between the exciton transistor300and field-effect transistors, the terminology of transistors will be employed.

The exciton transistor100comprises an exciton channel302, pads304, a gate306, a source308, and a drain310. The gate306, source308, and drain310all represent optical waveguides which extend beyond the region shown. The source waveguide308carries the signal that is to be switched. The source waveguide308, in some embodiments, comprises a steady flow of light such as that coming from a CW laser. The drain waveguide310carries the fraction of this light that has made it through the device: that is, the light that has been modulated or switched on or off. The gate waveguide306carries the light signal that performs the switching.

The pads304inFIGS.3-4can be gold pads that serve two functions. The first function is to provide a pad304to which the exciton channel302can be attached to during assembly of the optical switch300. The second function is to serve as a coupler that converts photons into excitons and vice versa.

Taking the source end of the exciton channel302as an example, the electric field of the incoming light field can be concentrated on the gold pad304. On the gold pad304this concentrated electric field can be referred to as a plasmon field. The concentrated electric field induces electric field oscillations in a row of dye molecules406within the exciton channel302. In terms of the quanta of these fields, the coupler can be said to make two transformations. The first transformation is to convert a photon into a plasmon; the second transformation is to convert a plasmon into an exciton. By concentrating the electric field, the conversion of incoming photos into excitons is more efficient than if the exciton channel302were connected directly to the source waveguide308. The coupler is a reciprocal device, meaning that it converts excitons into photons as efficiently as it converts photons into excitons. Hence, excitons arriving at the drain waveguide310of the optical switch300are transformed by the coupler into photons that then propagate away along the drain waveguide310.

The exciton channel302can be a DNA origami nanotube400(FIGS.5-6) containing a row of dye molecules406along a length of the DNA origami nanotube400. The purpose of the DNA origami nanotube400is to transport the energy of the photons arriving via the source waveguide308past the gate waveguide306and to the drain waveguide310. This energy is transported in the form of excitons.

DNA origami is a DNA nanotechnology fabrication technique. One example of DNA origami is described in Rothemund, “Folding DNA to Create Nanoscale Shapes and Patterns,” Nature 2006, 440, 297-302, which is herein incorporated by reference. Rothemund illustrates inFIGS.1(c) and1(e)of his publication a technique that employs a long single strand of DNA called a scaffold strand. The scaffold strand's base sequence can be regarded as pseudorandom. Such strands are often obtained from bacteriophages (viruses that infect bacteria). A convenient source for such DNA is the M13 bacteriophage since it packages its genome as single-stranded DNA. Viruses can be cultured, extracted, and their DNA purified. Conveniently, single-stranded M13 bacteriophage genomic DNA are now commercially available. Although the base sequence of the M13 bacteriophage codes for proteins and therefore has meaning biologically, from a technological point of view the base sequence statistics are close to that of a random sequence of bases (a random sequence of the four letters A, C, G, and T). Hence, it is a pseudorandom sequence. But because the M13 bacteriophage's genome has been sequenced, the DNA sequence has since become known.

Thereby, it is now possible to design short DNA strands, called staple strands, whose base sequences are complementary to certain regions of the scaffold strand by design. The base sequences for the staple strands are designed using the known DNA sequence of the scaffold strand and are produced by automated DNA synthesis machines. Such staple strands can be purchased commercially from foundries. One can, as an example, communicate the base sequences of the desired DNA strands to the foundry and the corresponding DNA strands are then produced by an automated DNA synthesis machine. These staple strands are designed to bind uniquely to specific regions on the scaffold strand. Examples of these are the short colored strands seen inFIGS.1(c) and1(e)of Rothemund.

Other options are also available for producing large origami structures, and for the case here DNA nanotubes400that can serve as substrates312for the dyes composing the exciton channel302. Some methods for making DNA origami scaffolds, such as the use of bacteriophage-based ssDNA production, have resulted in producing scaffolds as large as 31,274 nucleotides (nt). ssDNA 31,274 nt long has a length of 11,000 nanometers or 11 microns. Folded 5 times yields scaffolds of length 2.2 microns. This is more than sufficient to span the distance between the source and drain waveguides308,310ofFIGS.3-4.

By these means, the long scaffold strand can be folded into a geometrical shape. This assembly occurs in an aqueous solution consisting of a buffer containing salt. The scaffold strand and the staple strands are mixed together in the solution. The scaffold strand and the staple strands diffuse in the solution and encounter each other and complementary base sequences combine (the technical term is hybridize) to spontaneously form the geometric shape. To obtain the desired shapes in high yield, the solution is heated to above the melting temperature (the temperature at which duplex DNA dissociates into single strands) and then slowly cooled to room temperature. The melting temperature depends on the length of the complementary regions of DNA but for the short staple strands employed in DNA origami, heating to a temperature somewhere in the range of 60° C. to 90° C. is sufficient.

FIG. 2 of the Rothemund publication illustrates the capability of the DNA origami assembly technique. The first row indicates the layout of the scaffold strand to form the desired shape. The second row shows the predicted pattern when the staple strands are added. The third row shows atomic force microscope (AFM) images of the actual shapes produced. The fourth row illustrates some phenomena observed with AFM imaging, such as distortion of the origami in column a. The aggregation of origami by the “sticky” ends of the duplex DNA strands of the DNA origami, as shown in the Rothemund publication as columns b-e, and the well-behaved nature of the shape in column f due to the fact that this structure presents no sticky ends.

Although the structures Rothemund produced in his initial published work were planer 2-dimesional objects, this technique can be extended to produce 3-dimensional objects. Of interest here is the formation of DNA nanotubes suitable for purposes of fabricating the ballistic exciton transistor100and optical switch300described herein that can serve as substrates on which dye molecules406can be arranged. In other words, DNA origami can be used to assemble DNA nanotubes, including the DNA nanotubes400shown inFIGS.5-6.

In some embodiments, in order to produce a DNA nanotube of sufficient length, the overall structure can comprise two DNA nanotubules400(formed form M13 bacteriophage scaffold strands) spliced together. The two DNA origami nanotubes, individually, can be approximately 400 nanometers in length, whereas the overall structure can be approximately 800 nanometers in length.

It is worth notingFIGS.1(a) and4(d)of Douglas et al., “DNA-nanotube-induced alignment of membrane proteins for NMR structure determination,” PNAS 2007, 104, 6644-6648, which is herein incorporated by reference in its entirety, indicate the overall structure of the DNA-nanotube which can be thought of as six parallel duplex-DNA strands that are held together by stable strands that cross over from one duplex DNA strand to another.FIG.1(c)of Douglas et al. shows a layout of the two scaffold DNA strands.FIGS.1(e) and1(f)of Douglas et al. show how the staple strands are laid relative to the scaffold strands. A repetitive motive is used as indicated byFIG.1(b)of Douglas et al.

The number of parallel duplex strands making up the nanotube can be varied. In Douglas et al., a tube consisting of six such DNA strands was chosen, often referred to as a six-helix bundle. The size of the inter diameter of the tube can be varied by changing the number of duplex stands making up the bundle.

With reference toFIGS.5-6of the present disclosure, a five-helix bundle DNA nanotube400is most preferred for construction of the exciton channel302. However, it is envisioned that other numbers of helix bundles may provide similar and/or distinct benefits, and selection of an optimal number of helix bundles will depend upon the application in which the nanotube is being utilized. The diameter of a duplex strand of DNA402can be approximately two (2.0) nanometers. The inner diameter of this nanotube400can be approximately one and four tenths (1.4) nanometers, a size that is comparable to the size of a typical organic dye molecule406.

Dyes406can be attached at specific points along the DNA402. Keeping in mind that duplex DNA402is often a helical structure (e.g., the double helix), staple strands can be designed such that when the DNA nanotube400self-assembles, the attachment of the dye molecules406is at points on the inside of the DNA nanotube400. The dye molecules406will thus be on the inside of the nanotube400, as shown inFIGS.5-6. The spacing between bases in DNA is 0.34 nm and roughly 10 bases form one complete turn of the double helix. With a five-helix bundle nanotube400the stable strands can be designed such that the dyes will be stacked with a spacing of 0.34 nm. Close spacing between dyes406is desirable in that it increases the exciton exchange energy between dyes406which, in turn, causes the exciton to propagate more quickly and with less energy loss through the exciton channel302.

Software can be used to aid the design of DNA origami structures such as the nanotube400considered herein. One example of such software is CanDo (Computer-aided engineering for DNA origami). The design of origami structures is thus a task that can be largely automated. Examples of dyes, available commercially, that can be attached to DNA and that can serve as the dyes that constitute the exciton channel are the Cyanine dyes Cy5 and Cy5.5, but many more dye types are available and those skilled in organic chemistry can synthesis their own custom dyes that can be incorporated into DNA via covalent bonds during the synthesis of the DNA402.

The molecules brcan also comprise other dyes, and more particularly, the chromophores of said dyes. For example, chromophores that can be used include one or more of a xanthene, fluorescein, rhodamine, oregon green, eosin, Texas red, cyanine, indocarbocyanine, oxacarbocyanine, thiacarbocyanine, merocyanine, squaraine, Seta, SeTau, Square dyes, naphthalene, dansyl, prodan, coumarin, oxadiazole, pyridyloxazole, nitrobenzoxadiazole, benzoxadiazole, anthracene, anthraquinone, DRAQ5, DRAQ7, CyTRAK Orange, pyrene, cascade blue, oxazine, Nile red, Nile blue, cresyl violet, oxazine 170, acridine, proflavin, acridine orange, acridine yellow, arylmethine, auramine, crystal violet, malachite green, tetrapyrrole, porphin, phthalocyanine, and bilirubin, and/or a combination thereof.

Methods to attach DNA402to gold surfaces304include methods by which the exciton channel302is connected between at least two gold pads304. Topography can also be used to control nanotube400alignment.

Dipole Moments

The difference static dipole-dipole interaction, resulting from differences in the charge density of a molecule when it is in its excited state compared to when it is in its ground state, is employed. Dye404and the most proximal dye406to the gate region306must have difference static dipole moments.

In order to function as an exciton channel302that can be gated, the dye molecules404and406, the latter the channel dye that is proximal to the gate region306must have a difference static dipole moment that is large, preferably comparable to the transition dipoles involved in exciton exchange104. Organic dyes can have transition dipoles as high as 16 D, where D denotes the unit “debye” which is used to measure the strength of electric dipole moments. Asymmetry in the conjugated π-bond network of an organic dye molecule facilitates the position of a large difference static dipole moment that is large and hence yields exciton-exciton interactions104between dyes. Examples of dyes having an asymmetric conjugated π-bond network and that are commercially available for attachment to DNA are family of dyes offered by Dyomics, such as the dyes DY-550 through DY-831. This range of dyes allows the selection of dyes having optical transition frequencies close to frequencies of the light signals110that are to be switched. A number of organic molecules that have been theoretically calculated to have difference static dipole moments as large as 16 D are descried in Jacquemin, “Excited-state dipole and quadrupole moments: TD-DFT versus CC2,” J. Chem. Theory Comput. 2016, 12, 3993-4003, herein incorporated by reference in its entirety.

See, e.g., molecular structure 17 in Jacquemin's scheme 2 and the corresponding entries in their Table 3 where different calculational methods consistently predict large difference static dipole moments, around 16 D. The difference static dipole moments can also be referred to as “excess dipole moments.”

Beneficially, the present disclosure notes functional groups can be added to these compounds in such a way that they can be covalently attached to DNA during DNA synthesis without significantly altering the optical properties of the molecules.

The gate region306also contains a special dye molecule404(or several such dye molecules) depicted as the ellipsoid ofFIGS.5-6, in contrast to the dyes406of the exciton channel302, which are depicted in the row of ellipsoids. It is the special dye404and proximal406dye that give rise to the exciton-exciton interaction108responsible for switching, that is, excitons residing on these dyes block the flow of excitons in the exciton channel302. In order for this gate to function properly the exciton residing on the gate dye404must be prevented from hoping to the exciton channel302via the exchange interaction108. This can be accomplished by orienting the dye404such that its transition dipole is orthogonal to that of the transition dipoles in the exciton channel302. This is illustrated inFIGS.5-6by depicting the ellipsoid axis of the two types of dyes to be orthogonal, that is, the ellipsoids of the exciton channel dyes are oriented with their short axis parallel to the exciton channel, whereas the gate dye is oriented with its short axis perpendicular to the exciton channel axis. The gate dye404is shown maintaining its orientation by being sandwiched between two of the DNA duplex strands402. The position at which this dye must be attached to a DNA stable strand402to maintain this configuration can be determined during the DNA origami design process. An additional requirement is that the exciton-exciton interactions104not go to zero when the exciton exchange interaction108between the gate dye404and the channel dyes406is zero. This requires that the difference static dipole moment not be parallel to the transition dipole for at least one of either the proximal channel dye406or the gate dye404.

For typical dye molecules406the conjugated π-bond network is approximately linear and as a consequence the difference static dipole moment and the transition dipole tend to both be collinear with the long axis of the conjugated π-bond network. There are, however molecules for which the difference static dipoles and transition dipoles are not parallel. An example for which the two dipoles are perpendicular to each other is given by molecule 28 in scheme 2 of Jacquemin. This molecule is shown as follows:

For this molecule, the difference static dipole moment lies parallel to the horizontal axis while the transition dipole lies parallel to the vertical axis. Applicant has verified the strength of the difference static dipole moment for this molecule is approximately 8 D. Although Jacquemin did not report the value of the transition dipole moment, Applicant has calculated via time-dependent density functional theory (TD-DFT) that the molecule has a transition dipole moment of 4 D. When used as a gate molecule404, a small transition dipole moment is not serious because the molecule404is not being used as part of the exciton channel302. A difference static dipole moment of 8 D would be adequate for switching. Because the difference static dipole moment for this gate molecule404is perpendicular to its transition dipole moment, the gate molecule404can be oriented such that its transition dipole is orthogonal to the transition dipole moments of the exciton channel dipoles while its difference static dipole moment is close to parallel with that of the channel dyes, thereby giving rise to a large exciton-exciton interaction108.

Other Non-Limiting Examples of Excitonic Devices that can Employ the Excitonic Ballistic Transistor

It is to be appreciated that exciton wires may be formed when a series of chromophores are held within the architecture so that when a first chromophore, the “input chromophore,” is excited and emits an exciton, the exciton passes, without loss of energy if sufficiently close, to a second chromophore. That chromophore may then pass the exciton to a third chromophore, and so on down a line of chromophores in a wavelike manner. The wires may be straight or branched and may be shaped to go in any direction within the architecture. The architecture may contain one or more wires. Depending on the architecture system used, the exciton wires may be formed along a single nucleotide brick, such as in using the scaffold strand of nucleotide origami, or multiple bricks may comprise the wire, such as in molecular canvases. When two or more wires are brought sufficiently close to each other such that they are nanospaced, the exciton may transfer from one wire to the other. By controlling this transfer, it is possible to build quantum circuits and gates. Some examples of said quantum circuits and gates are described in co-owned, co-pending U.S. patent application Ser. No. 17/447,839, titled ENTANGLEMENT OF EXCITONS BY ACOUSTIC GUIDING, filed Sep. 16, 2021. The originally filed contents of U.S. patent application Ser. No. 17/447,839 are hereby incorporated by reference in their entirety including without limitation, the specification, claims, and abstract, as well as any figures, tables, appendices, or drawings thereof. Quantum algorithms enable the speed-up of computation tasks such as, but not limited to, factoring and sorting. These computations may be performed by an excitonic quantum computer. The excitonic quantum computer can be made from exciton coherence wires, circuits, and gates, such as those described in co-pending, co-owned U.S. Pre-Grant Pub. No. 2019/0048036, which is herein incorporated by reference in its entirety.

Exciton wires can be made by closely spacing chromophores brtogether as depicted inFIG.1row102. As discussed above, when chromophores are nanospaced apart, an exciton may transfer from one chromophore to another without the loss of energy. An exciton created at one end of the row of chromophores102may propagate down the row, hopping from one chromophore nanospaced to the next. This is done in a wavelike manner.

Exciton circuits made from these exciton wires may be made to be analogous to electronic circuits but where excitons carry the signals rather than electrons in classical computing. By bringing two exciton wires sufficiently close to each other an exciton can hop from one wire to the other by transferring from one chromophore to another. By doing this carefully one can make devices that function as signal dividers such as those found in Yurke et al., “Passive Linear Nanoscale Optical and Molecular Electronics Device Synthesis from Nanoparticles, 2000, Phys. Rev. A, 81, 033814, which is herein incorporated by reference in its entirety. The division ratio depends on rates with which excitons can be transferred between chromophores in the coupling region. The transfer rate depends on the spacing between the chromophores and their orientations. This dependence on spacing and orientation enables the construction of signal dividers with, for practical purposes, any division ratio. An exciton propagating down one exciton wire will become delocalized so that one must think of the exciton as being in a superposition state where it resides on both exciton wires. This excitonic device is a basis-change gate. The function of which is analogous to that of an optical beam splitter or microwave directional coupler. A basis-change gate is one of the fundamental quantum gates.

Another quantum gate of fundamental importance is a phase-shift gate. The phase accumulated by an exciton is proportional to the distance it travels. Hence, a phase-shift gate can simply be made by engineering the wire that the exciton travels over to have the length needed to accumulate the proper amount of phase. The phase an exciton accumulates is also determined by its energy relative to the optical transition energy for the chromophore. The optical transition energy here denotes the energy difference between the chromophore's ground electronic state and its lowest excited electronic state that has an allowed optical transition. Hence, phase shifters can also be fashioned choosing the chromophores of differing optical transition energies. It is also possible to make phase shifters by terminating two ports of a signal divider with chromophores having differing optical transition energies.

Another quantum gate of fundamental importance is a controlled basis change gate. In contrast to the gates already discussed, which rely on wave interference effects, a controlled basis change gate relies on the interaction between two excitons. When two excitons reside on neighboring chromophores they feel each other's presence just like two electrons will feel each other's Coulomb repulsion when they are brought close together. The two-exciton interaction arises from static Coulomb interactions between molecules and is most strong when the molecules have an asymmetric molecular structure. Asymmetric molecules possess a permanent electric dipole which changes sign when the molecule is excited from the ground state to the excited state. The static Coulomb interaction, in this case is a dipole-dipole interaction which, when both chromophores are excited (the two-exciton case), differs in sign from the case when only one chromophore is excited (the one-exciton case). Due to the static Coulomb interactions between chromophores one exciton will accumulate extra phase in the presence of the other exciton. As a result, the presence or absence of one exciton can control how the other exciton moves through a basis change gate.

These three types of gates, the basis-change gate, the phase-shift gate, and the controlled basis-change gate, form a complete set if the phase-shift gates can be produced with a finite set of phase angles. Because the phase angles can be controlled by the exciton path length, the optical transition energies of the phase-shifter wire chromophores, or through the construction of optical phase-shifter gates out of basis-change gates with selected ports terminated, this last requirement can be met. With this finite set of gates, one can assemble exciton circuits that perform any quantum computation. A set of gates having this property is said to be capable of universal quantum computation. This is analogous to the electronic computer case where the NAND gate is a universal gate in that any Boolean function can be implemented by a circuit employing only NAND gates.

It is possible to perform universal quantum computation with just basis-change gates and phase-shift gates, but the number of parts (gates) one needs grows exponentially with the size of the problem. So, doing quantum computation this way performs as well as classical computers. By introducing controlled basis-change gates one can drastically reduce the parts count so that much fewer parts are required than for a classical computer. The controlled basis-change gate enables the entanglement of many-body (many-exciton) states so that a network of quantum gates acts as if it is performing many different computations simultaneously. This is similar to an n bit memory register. In a classical computer each memory element of the register can be in either a “zero” or a “one” state but not both simultaneously. In contrast a quantum mechanical register can be in a state that is a quantum mechanical superposition of being in the zero state and the one state. An n bit quantum memory in this sense can act as if it is holding 2n bits of information, whereas the classical computer memory only holds n bits of information. A single controlled basis-change gate accepting as inputs the contents of memory elements i and j and delivering the outputs back to memory elements i and j can update the amplitudes of all of the 2n states in the superposition of the memory register simultaneously. This is quantum parallelism.

Not all math problems are known to benefit from quantum speedup, but several classes of problems are known where quantum computers can vastly outperform classical computers. Two of the problems are factoring and database searching.

Chromophores, however, exhibit many non-ideal characteristics for quantum computing. The electronic degrees of freedom are strongly coupled to the vibrational and environmental degrees of freedom. This causes phase jitter, which causes phase error to grow with time, thus spoiling the interference effects that the quantum gates relay on. All quantum computers suffer from this problem to a greater or lesser extent. Chromophores are also difficult to arrange in the requisite configurations.

What exciton quantum computers have in their favor is fast switching time, compact size (the components are relatively small molecules), and possible room temperature operation. Because photons are readily converted into excitons and excitons are readily converted into photons, it is noted that the above excitonic devices may find application in optical information processing, apart from quantum computing, as more compact embodiments of the currently employed optical phase shifters, signal dividers, and switches that can employ Kerr nonlinearities, which have the functionality of controlled basis-change gates. For these applications the performance requirements are less demanding than that for quantum computation.

Finally, it is to be appreciated Applicants have created compositions of non-reciprocal optical devices comprising of aggregates of chromophores either attached to a nucleotide architecture or covalently bonded having a desired conformation, such as those described in co-owned, co-pending U.S. patent application Ser. No. 17/443,285, titled MOLECULAR AGGREGATE FOR OPTICALLY-PUMPED NONRECIPROCAL EXCITON DEVICES, filed Jul. 23, 2021. The originally filed contents of U.S. patent application Ser. No. 17/443,285 are hereby incorporated by reference in their entirety, including without limitation, the specification, claims, and abstract, as well as any figures, tables, appendices, or drawings thereof.

From the foregoing, it can be seen that the present invention accomplishes at least all of the stated objectives.

LIST OF REFERENCE CHARACTERS

The following table of reference characters and descriptors are not exhaustive, nor limiting, and include reasonable equivalents. If possible, elements identified by a reference character below and/or those elements which are near ubiquitous within the art can replace or supplement any element identified by another reference character.

TABLE 1List of Reference Charactersagate moleculebmoleculer (e.g. −2, −1, 1, 2)position of molecules along the transmission lineJstrength parameter of exciton exchange interactionKstrength parameter of two-body exciton interaction100ballistic exciton transistor102exciton transmission line104exciton exchange interaction (e.g., a linear excitonexchange interaction)106gate108two-body exciton interaction110incoming signals112reflected signals114transmitted signals200plot300optical switch302exciton channel304coupler (e.g., gold pads)306gate waveguide/region308source waveguide/region310drain waveguide/region312substrate400nanotube402duplex strand of DNA404special dye molecule (e.g., a type of gate molecule a)406dye molecules (e.g., a row of molecules b)

Glossary

Unless defined otherwise, all technical and scientific terms used above have the same meaning as commonly understood by one of ordinary skill in the art to which embodiments of the present invention pertain.

The terms “a,” “an,” and “the” include both singular and plural referents.

The term “or” is synonymous with “and/or” and means any one member or combination of members of a particular list.

The terms “invention” or “present invention” are not intended to refer to any single embodiment of the particular invention but encompass all possible embodiments as described in the specification and the claims.

The term “about” as used herein refer to slight variations in numerical quantities with respect to any quantifiable variable. Inadvertent error can occur, for example, through use of typical measuring techniques or equipment or from differences in the manufacture, source, or purity of components.

The term “substantially” refers to a great or significant extent. “Substantially” can thus refer to a plurality, majority, and/or a supermajority of said quantifiable variable, given proper context.

The term “generally” encompasses both “about” and “substantially.”

The term “configured” describes structure capable of performing a task or adopting a particular configuration. The term “configured” can be used interchangeably with other similar phrases, such as constructed, arranged, adapted, manufactured, and the like.

Terms characterizing sequential order, a position, and/or an orientation are not limiting and are only referenced according to the views presented.

In mesoscopic physics, “ballistic conduction” (ballistic transport) is an unimpeded flow (or transport) of charge carriers (usually electrons), or energy-carrying particles, over relatively long distances in a material. In general, the resistivity of a material exists because an electron, while moving inside a medium, is scattered by impurities, defects, thermal fluctuations of ions in a crystalline solid, or, generally, by any freely-moving atom/molecule composing a gas or liquid. Without scattering, electrons obey Newton's second law of motion at non-relativistic speeds. Here, the definition is extended to excitons that propagate without energy loss.

A “chromophore” is the part of a molecule responsible for its color. The chromophore is a region in the molecule where the energy difference between two separate molecular orbitals falls within the range of the visible spectrum. Visible light that hits the chromophore can thus be absorbed by exciting an electron from its ground state into an excited state. In biological molecules that serve to capture or detect light energy, the chromophore is the moiety that causes a conformational change of the molecule when hit by light.

A “J-aggregate” is a type of dye with an absorption band that shifts to a longer wavelength (bathochromic shift) of increasing sharpness (higher absorption coefficient). In “H-aggregates”, a hypsochromic shift is observed with low or no fluorescence. Bathrochromically shifted “J-bands” and hypsochromically shifted “H-bands” have been explained in terms of molecular exciton coupling theory, i.e., coupling of transition moments of the constituent dye molecules. J and H aggregates can aggregate under the influence of a solvent or additive or concentration as a result of supramolecular self-organization. J and H aggregates can alternatively be formed by templating dyes to a scaffold such as DNA to control their proximity and orientation. Thus, it is to be appreciated the present disclosure is not to be limited to solely the aggregation phenomena to a self-organizing process.

A “bathochromic shift” is often referred to as a “red shift” in photochemistry. Bathochromic shifts are a change of spectral band position in the absorption, reflectance, transmittance, or emission spectrum of a molecule to a longer wavelength (lower frequency). Hypsochromic shifts are often referred to as “blue shifts” in photochemistry. Blue shift is the phenomenon in which the frequency of an electromagnetic wave, such as light, emitted by a source moving towards the observer is shifted towards the blue side of the electromagnetic spectrum (wavelength is decreased or energy is increased).

The “scope” of the present invention is defined by the appended claims, along with the full scope of equivalents to which such claims are entitled. The scope of the invention is further qualified as including any possible modification to any of the aspects and/or embodiments disclosed herein which would result in other embodiments, combinations, subcombinations, or the like that would be obvious to those skilled in the art.