# Patent

## Title
Delayed optical logic gates for boolean algebra

## Abstract

A system, method, and apparatus for delayed optical logic gates based on slow light and enhanced nondegenerate four-wave mixing processes, where a single or multiple delayed optical routers are utilized for dark resonance interactions in which two-color lasers interact with a three-level nonlinear optical medium comprised of two ground states and one excited state through the nondegenerate four-wave mixing processes. The delayed optical logic mechanism is based on combination of single or multiple dark resonance-induced two-photon coherence conversion via slow light phenomenon. The two-photon coherence induced on the ground states is optically detected via nondegenerate four-wave mixing processes. The nondegenerate four-wave mixing generation is enhanced owing to dark resonance or electromagnetically induced transparency. The delayed optical logic gates have potential to keep up ultra-high-bandwidth optical information processing using relatively slow electronic processing devices.

## Background
CLAIM OF PRIORITY
This application is a divisional application of U.S. patent application Ser. No. 12/280,923, “DELAYED OPTICAL LOGIC GATES,” filed on Aug. 27, 2008, by Ham, which claims priority to Korean Patent Application No. 10-2007-0126380 filed on Dec. 6, 2007, Korean Patent Application No. 10-2007-0126381, filed on Dec. 6, 2007, and PCT Patent Application No. PCT/KR2007/006846 filed on Dec. 26, 2007, all of which are incorporated herein by reference.


BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method and apparatus for delayed optical logic gates, where the physics lies in quantum-coherence-based slow light and enhanced nondegenerate four-wave mixing processes.
2. Description of the Related Art
In an electronic transistor, the switching time is determined by the carriers' transfer time across a gate, where the size of the transistor gate has been decreased for last three decades. This is called Moore's law and has been succeeded. Nowadays silicon semiconductor technologies are migrating into photonics, and this trend is called silicon photonics. In the fiber-optic communications, most optical devices are controlled by electric current or electric voltage, where the control circuit is Si-based electronics. However the electronics is much slower than optics. Thus speed constraint of an electrooptic device lies in the electronics. Recently, quantum switch and photon logic gates are introduced to overcome such limitations in the switching technologies: B. S. Ham, U.S. Pat. No. 6,628,453 (2003); B. S. Ham, PCT patent filing number PCT/KR2007/001130 (2007).
On the other hand, in fiber-optic communications, optical switching technologies have been rapidly evolved for faster switching components. In this optoelectronics area electronic counterpart is lagged behind in speed itself. Thus overall performance of all-optical switching devices is should be slowed down. Obviously computer-based electro-optic device has the speed constraint on the electronics.
To overcome such unbalance between optics and electronics, buffering techniques have been introduced. This buffering method is to delay the fast optical data traffic on demand for the relatively slow electronic components. Thus, adjustable buffering memory techniques are expected. Unfortunately all-optical active buffer memory has not been implemented, yet. Most of the suggested ideas, inventions or devices, however, are passive like such as using a bundle of fiber-optic cables and a ring resonator on a silicon waveguide.
It is well known that resonant two-color electromagnetic fields can induce a refractive index change in a nonlinear optical medium composed of three energy levels or more. In a three-level optical system composed of two-closely spaced ground states, the refractive index change can result in not only absorption cancellation at line center but also two-photon coherence excitation on the ground levels. This phenomenon is called dark resonance or electromagnetically induced transparency (EIT) in the context of optically dense medium: S. E. Harris, Phys. Today. Vol. 50 (No. 7), p. 36 (1997); Phys. Rev. Lett. Vol. 62, pp. 1033-1036 (1989)). Because EIT modifies the absorption spectrum of an optical medium, the medium's dispersion must be also modified via Kramers Kronig relations. The modified dispersion profile directly affects on a group velocity of a traveling light pulse through the optical medium. This is so called a slow light phenomenon. Recently the slow light phenomenon has been observed in cold atoms (Hau et al., Nature Vol. 397, pp. 594-598 (1999)), defected solids (B. S. Ham et al., Phys. Rev. Lett. Vol. 88, p. 236024 (2002), s fiber-coupled resonator (Totsuka et al., Phys. Rev. Lett. Vol. 98, p. 213904 (2007), and semiconductors (Wang et al., Opt. Lett. Vol. 29, pp. 2291-2293 (2004).
An optical router is a switching device converting an optical signal into another one at different propagation directions with either the same frequency basis or not. The optical router is a subcategory of an optical switch that is in general used to drop, add, multiplex, or convert an optical signal into another one. In fiber-optic communications, as more data traffic is demanded, more information bandwidth is needed. In this case a wider bandwidth optical switch is obviously expected. So far optical switching speed is already passed over 60 GHz, which is much faster than a Pentium CPU. Thus, more often it is required that the data traffic in fiber-optic communication lines need to be temporally delayed for some data processing purposes. Obviously, an optical buffer memory becomes an essential component to an optical data processing unit.
A delayed optical router has been suggested. According to the delayed optical router, a slow light is used for routing via nondegenerate four-wave mixing processes. Thus the delayed optical router can delay the input data up to the group delay time, which is the delay time can be controllable by adjusting coupling light intensity C in FIG. 1: Ham et al., Physical Review Letters, Vol. 88, p. 236024 (2002).
SUMMARY OF THE INVENTION
The primary object of the present invention is to provide a method and apparatus of a delayed optical logic gates. The main characteristic of the delayed optical logic gates is that the logic operation is based on the slow light and nondegenerate four-wave mixing processes, where the slow light excites quantum coherence on the ground states and this quantum coherence is retrieved into photon component via the wave-mixing processes. Here, it should be noted that the slowdown factor does not degrade the overall data traffic rate at all, because the data traffic rate across the delayed optical switch/router should be same. It means that the switching/routing bandwidth is invariant to the slowdown factor in the present invention. Moreover, the slow group velocity is a direct result of medium's dispersion modification due to EIT or coherent population oscillations (Boyd et al., Science Vol. 301, pp. 200-202 (2003)). Therefore, the optical delay time in the present invention of the delayed optical logic gates is actively controllable. Actually this function of the slowdown is the main function of an optical buffer memory. Hence, the present invention of the delayed optical logic gates includes the function of the optical buffer memory, too.
For better understanding of delay optical logic operation, let's carefully study how incoming optical data traffic behaves at the interfaces of a nonlinear optical medium used for the present delayed optical logic gates. At the front interface of it, the data traffic incident becomes slow down depending on the group velocity. In more detail, the front part of an optical pulse envelope incident to an optical medium of the delayed optical router starts to be compressed in both space and time until the back end of the pulse envelope enters the medium. The compressed optical pulse now propagates through the medium in a slow speed until it reaches at the back end of the medium. Here it should be noted that consecutive optical pulse entering the nonlinear medium does not collide with each other at the interface even though the propagation velocity is very different. When the optical pulse leaves the medium at the back end, the front part of the optical pulse envelope now begins to fly forward in a very high speed until the back end of the pulse envelope leaves the medium. Therefore the data traffic rate across the delayed optical logic gates is invariant.
In the present invention of the delayed optical logic gates, several Boolean logic gates are claimed for NOT, OR, NOR, XOR, AND, and NAND in all-optically delayed regime. The primary object of the present invention is to provide a method and an apparatus of delayed optical logic gates based on slow light and nondegenerate four-wave mixing processes.
The delayed optical logic gates have functions of dynamically controllable delay-time of the incoming signal light using slow light phenomenon, where the delay-time of the logic gates is controllable by adjusting another coupling light intensity to affect on the group delay of the slow light. The switching time for each signal light pulse limits in phase decay time of the optical nonlinear medium (B. S. Ham, Applied Physics Letters, Vol. 85 (No. 6), pp. 893-895 (2004); Physical Review B, Vol. 68 (No. 7), pp. 023811 (2003); U.S. Pat. No. 6,628,453). However, the bandwidth of the delayed optical logic gates or overall gating speed is invariant of the group delay of the slow light because the bandwidth of ‘IN’ and ‘OUT’ across the nonlinear medium used for the delayed optical logic gates is same. Main advantage of the present invention of the delayed optical logic gates is the data delay-time controllability useful for a slow electronic device to alleviate processing power toward high-speed optical data rates.
Briefly described, a system of the delayed optical logic gates of the present invention is provided by multiply connected delayed optical routers composed of a nonlinear optical medium and coherent light pulses. The nonlinear optical medium of the delayed optical logic gates is composed of at least three-energy levels. Two of them should be closely spaced on the ground states, and the third one should be an excited state. The frequencies of the laser light of C and A are either same or different depending on purposes: See FIG. 1. The light pulse A is used as a control for nondegenerate four-wave mixing processes to generate the output pulse D. The nondegenerate four-wave mixing output D can be used as an input(s) to the second nonlinear medium to configure the present invention of the delayed optical logic gates. In FIG. 1 the output S is the slow light of the input light P. According to nondegenerate four-wave mixing process, S and D are alternative. Each light pulse can be guided by an optical waveguide, free space, or surface plasmon optical waveguide. The optical waveguide is not part of the current invention. By connecting two or more delayed optical routers, the present invention of the delayed optical logic gates performs the Boolean logic: NOT, NAND, AND, OR, XOR, and NOR. The delayed optical logic gates can be applied for scalability purposes. The transmission time between two delayed optical logic gates is negligible because the light pulse moves almost speed of light.
To achieve these and other advantages as described above and in accordance with the purpose of the present invention, this specification provides a method for operating a logical gate using at least one delayed optical router comprising a nonlinear optical medium, wherein the nonlinear optical medium comprises two closely spaced ground states such that a transition between said two ground states is dipole forbidden, and an excited state such that two-photon transitions between said two ground states via said excited state are allowed, the method comprising:
using at least one of a slow light (S) and a nondegenerate four-wave mixing signal (D) as a result of Boolean algebra,
wherein the slow light (S) is appeared by applying, to the nonlinear optical medium, a first laser beam (P) with a first frequency corresponding to a first transition between a first ground state of the two ground states and the excited state and a second laser beam (C) with a second frequency corresponding to a second transition between a second ground state of the two ground states and the excited state; and the nondegenerate four-wave mixing signal (D) is appeared by applying, to the nonlinear optical medium, the first laser beam (P) with the first frequency, the second laser beam (C) with the second frequency and a third laser beam (A) with a third frequency corresponding to the second transition.
This specification also provides a method of operating a logical gate using at least one delayed optical router comprising a nonlinear optical medium, wherein the nonlinear optical medium comprises two closely spaced ground states such that a transition between said two ground states is dipole forbidden, and an excited state such that two-photon transitions between said two ground states via said excited state are allowed, the method comprising: a) applying, to said nonlinear optical medium, a first laser beam (P) at a first frequency corresponding to a first transition between a first ground state of said two ground states and said excited state; b) applying, to said nonlinear optical medium, a second laser beam (C) at a second frequency corresponding to a second transition between a second ground state of said ground states and said excited state; c) applying, to said nonlinear optical medium, a third laser beam (A) at a third frequency corresponding to the second transition between the second ground state of said ground states and said excited state; d) adjusting an intensity of said second laser beam (C) to produce a slow light (S), wherein said slow light (S) corresponds to a group velocity slow down of said first laser beam (P); e) adjusting at least one of intensities of said first laser beam (P), said second laser beam (C), said third laser beam (A), to produce a nondegenerate four-wave mixing signal (D) at a frequency corresponding to a two-photon coherence excitation [Reρ12]2, wherein said slow light (S) is disappeared in response to the producing of said nondegenerate four-wave mixing signal (D); and f) using at least one of said produced slow light (S) and said nondegenerate four-wave mixing signal (D) as a result of a logical gate.
This specification also provides an apparatus for an optical logic gate, comprising;
at least one delayed optical router including at least one nonlinear optical media, wherein the nonlinear optical medium comprises two closely spaced ground states such that a transition between said two ground states is dipole forbidden, and an excited state such that two-photon transitions between said two ground states via said excited state are allowed;
at least one port for outputting a result of the optical logic gate,
wherein the result is represented as at least one or more of a slow light and a nondegenerate four-wave mixing signal (D),
the slow light (S) is appeared by applying, to the nonlinear optical medium, a first laser beam (P) with a first frequency corresponding to a first transition between a first ground state of the two ground states and the excited state and a second laser beam (C) with a second frequency corresponding to a second transition between a second ground state of the two ground states and the excited state; and
the nondegenerate four-wave mixing signal (D) is appeared by applying, to the nonlinear optical medium, the first laser beam (P) with the first frequency, the second laser beam (C) with the second frequency and a third laser beam (A) with a third frequency corresponding to the second transition.
The foregoing and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings.



BRIEF DESCRIPTION OF THE DRAWINGS
The accompanying figures illustrate several embodiments of the present invention, and together with the descriptions, serve to explain the principles of the invention. The drawings are only for the purpose of illustrating a preferred embodiment of the invention and are not to be construed as limiting the invention.
FIG. 1 (a) illustrates a block diagram of a delayed optical logic gate, NOT, of the present invention. FIG. 1 (b) illustrates the light pulse sequence. The relationship between 104 (S) and 105 (D) is a toggle switch.
FIG. 2 (a) shows an energy level diagram of the present invention of the delayed optical logic gates: FIG. 2 (b) shows a propagation scheme of the light for time-delayed scheme between 102 (C) and 103 (A).
FIG. 3 (a) shows a slow light S and FIG. 3 (b) shows a routed light D based on nondegenerate four-wave mixing processes: Delayed optical switching/routing. The spatial direction of the output light S and D is determined by the phase matching conditions of the input light P, C, and A in FIG. 1.
FIG. 4 illustrates a schematic diagram of a delayed optical logic gate, NOR, of the present invention. Letter DR stands for the delayed optical router comprised of a nonlinear optical medium 106 in FIG. 1, which is connected by optical waveguides, free space, or plasmon optical waveguide used for the laser beams P, C1, A, C2, B, S, D, X, and Y.
FIG. 5 illustrates a schematic diagram of a photon logic gate, AND, of the present invention. Letter DR stands for the delayed optical router comprised of a nonlinear optical medium 106 in FIG. 1, which is connected by optical waveguides, free space, or plasmon optical waveguide used for the laser beams P, C1, C2, A, B, S, D, X, and Y.
FIG. 6 illustrates a schematic diagram of a delayed optical logic gate, NAND/OR, of the present invention. Letter DR stands for the delayed optical router comprised of a nonlinear optical medium 106 in FIG. 1, which is connected by optical waveguides, free space, or plasmon optical waveguide used for the laser beams P, C1, C2, S, D, S1, D1, S2, D2, X, and Y.
FIG. 7 illustrates a schematic diagram of a delayed optical logic gate, NOR/XOR/AND, of the present invention. Letter DR stands for the delayed optical router comprised of a nonlinear optical medium 106 in FIG. 1, which is connected by optical waveguides, free space, or plasmon optical waveguide used for the laser beams P, C0, C1, C2, A, B, S, D, S1, D1, S2, D2, X, Y, and Z.



DESCRIPTION OF THE PREFERRED EMBODIMENTS
To get a better understanding, reference is now made to the drawings which illustrate the preferred embodiments of the present invention.
FIG. 1 (a) shows a delayed optical router as a basic building block for the present invention of the delayed optical logic gates.
FIG. 1(a) describes a delayed optical logic gate, NOT, where a single delayed optical router is used. Letters P, C, A, S, and D stand for light pulse at different propagation directions kP, kC, kA, kS, and kD, respectively. The numbers from 101 to 105 stand for lights as well as physical channels such as optical waveguide or free space used for the laser beams. The number 106 stands for a nonlinear optical medium. According to the delayed optical router, which will be explained below, the output S (104) is always OFF whenever the logical input light A (103) is switched ON, and vice versa. Here it should be noted that the light C may be continuous if the frequency of the light C is different from the light A. TABLE 1 shows the resulting Boolean algebra NOT of FIG. 1: The light C is always ON. Meanwhile, FIG. 1 (b) shows a pulse sequence.












TABLE 1







P
A
S (NOT)
D









1
0
1
0



1
1
0
1










FIG. 2 shows an energy level diagram of the nonlinear optical medium 106 of FIG. 1. The lower two closely spaced energy levels are resulted from the hyperfine splitting of most atoms or rare-earth doped crystals. The energy level structure of FIG. 2 can also be obtained easily in semiconductor quantum wells or quantum dots utilizing heavy hole and light hole for exciton transitions or trion transitions. The nonlinear optical medium 106 of FIG. 1 has either three energy states; |1>, |2>, and |3> or four energy states; |1>, |2>, |3>, and |4>, where the level |4> is either virtual or real. The state |3> of FIG. 2 is higher than |1> and |2> in energy. In fact the nonlinear optical medium 106 of FIG. 1 may have more than three energy levels, but only the mentioned energy levels shown in FIG. 2 contribute to the photon logic mechanism of the present invention.
The output light D at frequency ωD is generated by nondegenerate four-wave mixing processes, where three laser interactions of P, C, and A are involved at frequencies ωP, ωC, ωA, respectively, with the nonlinear optical medium.
Similarly, the output light S at frequency ωS is generated by electromagnetically induced transparency (EIT) or coherent population oscillations (CPO) due to modified absorption and dispersion spectra: Refer S. E. Harris, Physical Review Letters, Vol. 64, pp. 1107-1110 (1991) for EIT, and R. Boyd et al., Science Vol. 301, pp. 200-202 (2003) for CPO.
The propagation directions of the light are shown in FIG. 2 (b), and are determined by the phase matching conditions, respectively: kD=kC−kP+kA. Here, the nondegenerate four-wave mixing generation is strongly enhanced owing to dark resonance or EIT: Harris in Physical Review Letters, Vol. 64, pp. 1107-1110 (1991); Jain et al. in Optics Letters Vol. 18, pp. 98-101 (1993); Ham et al. in Optics Letters, Vol. 22, pp. 1138-1140 (1997). Signal amplifications and high-conversion efficiency using atomic gases for nondegenerate four-wave mixing processes were also experimentally demonstrated by Hemmer at al. in Optics Letters, Vol. 20, pp. 982-984 (1995) and Jain et al. in Physical Review Letters, Vol. 77, pp. 4326-4329 (1996), respectively. The high-conversion efficiency of nondegenerate four-wave mixing processes was also experimentally demonstrated in ion-doped solids by Ham et al. in Physical Review A, Vol. 59, pp. R2583-2586 (1999). The enhancement of nondegenerate four-wave mixing processes is based on reduced first-order linear susceptibility and enhanced third-order nonlinear susceptibility owing to destructive and constructive quantum interference, respectively.
To show more detail relations between the input signal light P and the nondegenerate four-wave mixing output light D, coherence mapping should be understood. To see the coherence excitation in FIG. 2, density matrix ρ must be discussed. The density matrix has been a useful tool to show a system's macroscopic ensemble; Quantum optics, Cambridge University Press, New York, N.Y. (1997), Edited by Scully and Zubairy.
In FIG. 2 (a), two laser beams C and P can induce two-photon coherence ρ12 on the transition |1>-|2> via the excited state |3>. The two-photon coherence is strongly enhanced if dark resonance or EIT involved. Here, dark resonance or EIT is the same physical phenomenon, but the term EIT roots in the absorption cancellation so that a resonant electromagnetic field can pass through an optically thick medium without experiencing any absorption. When coherent light A interacts with the nonlinear optical medium after the interaction for EIT, the two-photon coherence or dark resonance can be retrieved toward light P if the frequency of D is same as that of C: Ham et al, Opt. Lett. Vol. 22, pp. 1138-1140 (1997). Because coupling light C modifies the refractive index of the nonlinear optical medium 106 of FIG. 1, the dispersion profile is also modified, so that the group velocity of the signal light P can be slowed down: Hau et al., Nature Vol. 397, pp. 594-598 (1999) and B. S. Ham et al., Phys. Rev. Lett. Vol. 88, p. 236024 (2002). The slow light is denoted by S. The light propagation vectors of the light P and S is same each other.
FIG. 3 (a) shows a slow light S and FIG. 3 (b) shows a routed light D observed in Pr3+:YSO based on FIG. 2. This proves delayed nondegenerate four-wave mixing signal D, and the delayed light S can be used for delayed optical routing. E-P (E-A) stand for electric reference for P (A).
FIG. 4 (a) describes a delayed optical logic gate, i.e., NOR gate, where two-delayed optical routers are connected in series. Here, the output S (405) of the left (first) delayed optical router (DR1) is fed into the right (second) delayed optical router (DR2) as an input light (see P in FIG. 1). Two logical input light A (402) from DR1 and B (407) from DR2 perform optical logic inputs and result in Boolean algebra NOR at the output X (410). TABLE 2 shows the Boolean algebra of NOR resulted in the outputs X 410 by the combinations of two logic inputs A (402) and B (407). FIG. 4 (b) shows a pulse sequence.













TABLE 2





P
A
B
S
D
X (NOR)
Y







1
0
0
1
0
1
0


1
0
1
1
0
0
1


1
1
0
0
1
0
0


1
1
1
0
1
0
0









FIG. 5 (a) shows a delayed optical logic gate, i.e., AND gate, where the logic gate is composed of two delayed optical routers connected in series. Here, the output D (506) of the left delayed optical router DR1 (502) is fed into the right delayed optical router DR2 (507) as an input P (see P in FIG. 1). The combination of two logic input light A (503) from DR1 and B (508) from DR2 result in Boolean algebra AND to the output Y (511). TABLE 3 shows a resulting Boolean algebra AND appeared in the output Y (511) according to two logic inputs A (503) and B (508). FIG. 5 (b) shows a pulse sequence.













TABLE 3





P
A
B
S
D
X
Y (AND)







1
0
0
1
0
0
0


1
0
1
1
0
0
0


1
1
0
0
1
1
0


1
1
1
0
1
0
1









FIG. 6 (a) shows a delayed optical logic gate, i.e., NAND/OR gate. The system is composed of two-delayed optical routers connected in parallel, where the input light P (601) is shared. The output S1 (605) from the top delayed optical router DR1 and S2 (610) from the bottom delayed optical router DR2 is combined together to lead the logic output X (612). The outputs D1 (606) and D2 (611) are combined to lead the logic output Y (613). The signal light P (601) is split into two components through an optical splitter/combiner such as a Y branch or a beam splitter. Under the action of two inputs A (603) and B (608), the output logic X (612) and Y (613) perform Boolean logic operations NAND and OR, respectively: see TABLE 4. FIG. 6 (b) shows a pulse sequence.















TABLE 4





P
A
B
S1
D1
S2
D2
X (NAND)
Y (OR)







1
0
0
1
0
1
0
1
0


1
0
1
1
0
0
1
1
1


1
1
0
0
1
1
0
1
1


1
1
1
0
1
0
1
0
1









FIG. 7 (a) shows a delayed optical logic gate, i.e., NOR/XOR/AND gate. The system is composed of three delayed optical routers, where two of them are connected to the third one. Each output S (705) and D (706) of the delayed optical router DR0 is used as an input to the delayed optical routers DR1 and DR2, respectively. The output S1 (709) of the DR1 is used as a logic output X. The outputs D1 (710) and S2 (715) are combined together to lead the logic output Z (717). The output D2 (716) from the DR2 is used as a logic output Y. There are two logic inputs A (702) and B (708, 712), where A is for the DR0 and B is for both DR1 and DR2. As seen in TABLE 5, the two logic inputs A and B performs Boolean algebra NOR at the output X, XOR at Z, and AND at Y, simultaneously. FIG. 7 (b) shows a pulse sequence.


















TABLE 5














X

Z


S
A
B
S
D
X
D1
S2
Y
(NOR)
Y (AND)
(XOR)







1
0
0
1
0
1
0
0
0
1
0
0


1
0
1
1
0
0
1
0
0
0
0
1


1
1
0
0
1
0
0
1
0
0
0
1


1
1
1
0
1
0
0
0
1
0
1
0









As the present invention may be embodied in several forms without departing from the spirit or essential characteristics thereof, it should also be understood that the above-described embodiments are not limited by any of the details of the foregoing description, unless otherwise specified, but rather should be construed broadly within its spirit and scope as defined in the appended claims, and therefore all changes and modifications that fall within the metes and bounds of the claims, or equivalence of such metes and bounds are therefore intended to be embraced by the appended claims.

## Claims

1. A method for operating a logical gate using at least one or more delayed optical routers comprising a nonlinear optical medium, wherein the nonlinear optical medium comprises two closely spaced ground states such that a transition between the two ground states is dipole forbidden, and an excited state such that two-photon transitions between the two ground states via the excited state are allowed, the method comprising:
using at least one of a slow light (S) and a nondegenerate four-wave mixing signal (D) as a result of Boolean algebra,
wherein the slow light (S) is appeared by applying, to the nonlinear optical medium, a first laser beam (P) with a first frequency corresponding to a first transition between a first ground state of the two ground states and the excited state and a second laser beam (C) with a second frequency corresponding to a second transition between a second ground state of the two ground states and the excited state, and
the nondegenerate four-wave mixing signal (D) is appeared by applying, to the nonlinear optical medium, the first laser beam (P) with the first frequency, the second laser beam (C) with the second frequency and a third laser beam (A) with a third frequency corresponding to the second transition,
wherein two serial delayed optical routers are used for a Boolean AND algebra, the using at least one of a slow light (S) and a nondegenerate four-wave mixing signal (D) as a result of Boolean algebra includes:
inputting two third laser beams (A) respectively into the two serial delayed optical routers as respective inputs of the Boolean AND algebra,
inputting a first nondegenerate four-wave mixing signal (D), which is produced by a first delayed optical router of said two serial delayed optical routers, as a source of a first laser beam (P) of a second delayed optical router of the two serial delayed optical routers, and
using a second nondegenerate four-wave mixing signal (D) that is produced by the second delayed optical router as the result of the Boolean AND algebra.

2. An apparatus for an optical logic gate, comprising:
at least one or more delayed optical routers including at least one nonlinear optical media, wherein the nonlinear optical medium comprises two closely spaced ground states such that a transition between the two ground states is dipole forbidden, and an excited state such that two-photon transitions between the two ground states via the excited state are allowed;
at least one port for outputting a result of the optical logic gate,
wherein the result is represented as at least one or more of a slow light and a nondegenerate four-wave mixing signal (D),
the slow light (S) is appeared by applying, to the nonlinear optical medium, a first laser beam (P) with a first frequency corresponding to a first transition between a first ground state of the two ground states and the excited state and a second laser beam (C) with a second frequency corresponding to a second transition between a second ground state of the two ground states and the excited state; and
the nondegenerate four-wave mixing signal (D) is appeared by applying, to the nonlinear optical medium, the first laser beam (P) with the first frequency, the second laser beam (C) with the second frequency and a third laser beam (A) with a third frequency corresponding to the second transition,
wherein two serial delayed optical routers are used for a Boolean AND algebra,
wherein two third laser beams (A), which are respectively input to the two delayed optical routers, correspond to inputs of the Boolean AND algebra,
wherein a first nondegenerate four-wave mixing signal (D), which is produced by a first delayed optical router of said two serial delayed optical routers, is used as a source of a first laser beam (P) of a second delayed optical router of the two serial delayed optical routers, and
wherein a second nondegenerate four-wave mixing signal (D) is produced by the second delayed optical router and corresponds to the result of the Boolean AND algebra.

3. A method for operating an optical logic gate for a Boolean algebra, the method comprising:
generating at least one or more of a first laser beam (P) with a first frequency, a second laser beam (C) with a second frequency and a third laser beam (A) with a third frequency;
applying the at least one or more of the first laser beam (P), the second laser beam (C) and the third laser beam (A) to at least one or more delayed optical routers comprising a nonlinear optical medium,
wherein the nonlinear optical medium comprises two closely spaced ground states such that a transition between the two ground states is dipole forbidden, and an excited state such that two-photon transitions between the two ground states via the excited state are allowed,
wherein the first laser beam (P) with the first frequency makes a first transition between a first ground state of the two ground states and the excited state,
wherein at least one of the second laser beam (C) with a second frequency and third laser beam (A) with a third frequency makes a second transition between a second ground state of the two ground states and the excited state,
wherein if the first laser beam (P) and the second laser beam are applied to the at least one or more delayed optical routers, a slow light (S) is generated, and
wherein if the first laser beam (P), the second laser beam (C) and the third laser beam (A) are applied to the at least one or more delayed optical routers, a nondegenerate four-wave mixing signal (D) is generated; and
performing Boolean algebra calculations using at least one of the slow light (S) and the nondegenerate four-wave mixing signal (D),
wherein two serial delayed optical routers are used for a Boolean AND algebra, the performing Boolean algebra calculations using at least one of the slow light (S) and the nondegenerate four-wave mixing signal (D) includes:
inputting two third laser beams (A) respectively into the two serial delayed optical routers as respective inputs of the Boolean AND algebra,
inputting a first nondegenerate four-wave mixing signal (D), which is produced by a first delayed optical router of said two serial delayed optical routers, as a source of a first laser beam (P) of a second delayed optical router of the two serial delayed optical routers, and
using a second nondegenerate four-wave mixing signal (D) that is produced by the second delayed optical router of the two serial delayed optical routers as the result of the Boolean AND algebra.