Abstract:
An embodiment of the invention relates to a single-photon source for emitting single photons, comprising a cavity having a first mirror and a second mirror and exhibiting a longitudinal resonance frequency between the first and second mirror; at least one quantum dot arranged inside said cavity, said quantum dot being strain-dependent and configured to generate radiation at a strain-dependent radiation frequency; a device capable of exciting the quantum dot to generate radiation; a piezoelectric crystal being arranged outside the cavity and mechanically coupled to the second mirror&#39;s outer surface, said piezoelectric crystal configured to receive a control voltage and capable of applying either a laterally tensile and vertically compressive strain to both the cavity and the quantum dot, or a laterally compressive and vertically tensile strain to both the cavity and the quantum dot, depending on the control voltage&#39;s polarity; wherein, in response to said strain, the resonance frequency and the radiation frequency shift in opposite directions.

Description:
The invention relates to single-photon sources. Single-photon sources are photon sources which can emit single photons, particularly with a defined or predetermined polarization, transposed photons and cascades of correlated photons. 
     BACKGROUND OF THE INVENTION 
     Single-photon sources are the core element of quantum cryptography. In the exchange of sensitive data such as e.g. online business transactions, they offer absolute interception protection based on the laws of quantum mechanics. 
     An ideal single-photon source (photon gun) is a component which emits a single photon after a trigger signal, and only then (on demand). The central element of a single-photon source is optimally a quantized system with discrete energy levels. 
     German Patent Application DE 10 2008 036 400 describes a single-photon source having a cylindrical cavity. The cavity comprises a first mirror and a second mirror and exhibits a longitudinal resonance frequency between the first and second mirrors. The single-photon source emits photons efficiently only if the quantum dot&#39;s radiation frequency corresponds to the cavity&#39;s longitudinal resonance frequency. As such, the quality factor of the cavity needs to be limited since a large quality factor would reduce the chance that the radiation frequency matches the cavity&#39;s longitudinal resonance frequency. In summary, the tolerance range of this type of single-photon source is small, and the fabrication yield is poor. 
     OBJECTIVE OF THE PRESENT INVENTION 
     An objective of the present invention is to provide a single-photon source which has a larger tolerance range for fabrication than prior art single photon sources. 
     A further objective of the present invention is to provide a single-photon source that allows including cavities having a higher Q-factor than prior art single photon sources. 
     Furthermore, it is an objective of the present invention to provide a single-photon source that allows efficiently compensating temperature drifts. 
     BRIEF SUMMARY OF THE INVENTION 
     An embodiment of the present invention relates to a single-photon source for emitting single photons, comprising a cavity having a first mirror and a second mirror and exhibiting a longitudinal resonance frequency between the first and second mirror; at least one quantum dot arranged inside said cavity, said quantum dot being strain-dependent and configured to generate radiation at a strain-dependent radiation frequency; a device capable of exciting the quantum dot to generate radiation; a piezoelectric crystal being arranged outside the cavity and mechanically coupled to the second mirror&#39;s outer surface, said piezoelectric crystal configured to receive a control voltage and capable of applying either a laterally tensile and vertically compressive strain to both the cavity and the quantum dot, or a laterally compressive and vertically tensile strain to both the cavity and the quantum dot, depending on the control voltage&#39;s polarity; wherein, in response to said strain, the resonance frequency and the radiation frequency shift in opposite directions. 
     The cavity is oriented along and photon emission occurs in the vertical direction. A lateral direction is any direction that is perpendicular to the vertical direction along which the cavity is oriented and photons are emitted. A lateral direction is a direction in 3-dimensional space that is perpendicular to the vertical direction. 
     According to this embodiment of the invention, the resonance frequency and the radiation frequency are shifted in opposite directions in response to strain. This is achieved by applying the same kind of strain (laterally tensile and vertically compressive or laterally compressive and vertically tensile) to both the cavity and the quantum dot. As such, by applying a voltage of the appropriate polarity, the resonance frequency and the radiation frequency may always be brought to a match. Thus, it is not mandatory that the resonance frequency and the radiation frequency match exactly after fabrication of the single-photon source since a mismatch may later be corrected by simply applying a voltage to the piezoelectric crystal. Further, in case the temperature changes, any drift of the resonance frequency relative to the radiation frequency may be easily compensated. 
     The device capable of exciting the quantum dot to generate radiation may be a charge carrier injection device which is capable of injecting charge carriers into the cavity in order to excite the quantum dot to generate radiation. Alternatively the device may be an optical pump source which excites the quantum dot optically. 
     According to a preferred embodiment, the quantum dot is configured to increase its radiation frequency in case of laterally compressive and vertically tensile strain, and to decrease its radiation frequency in case of laterally tensile and vertically compressive strain. 
     The laterally tensile and vertically compressive strain preferably reduces the distance between the first and second mirror and increases the cavity&#39;s resonance frequency. The laterally compressive and vertically tensile strain preferably increases the distance between the first and second mirror and decreases the cavity&#39;s resonance frequency. 
     The photons are preferably coupled out of the cavity through the first mirror if the emission frequency corresponds to the longitudinal resonance frequency of the cavity. 
     The strain induced by the piezoelectric crystal inside the cavity and inside the quantum dot, is preferably biaxial. 
     The first and second mirror may each comprise distributed Bragg reflectors. 
     The piezoelectric crystal may have a surface section that is mechanically coupled to the second mirror&#39;s outer surface, and a given thickness. The size of the surface section preferably increases and the thickness preferably decreases if the control voltage has a first polarity, and the surface size of the surface section preferably decreases and the thickness preferably increases if the control voltage has an opposite second polarity. 
     The surface section of the piezoelectric crystal is preferably as large as the second mirror&#39;s outer surface or larger than the second mirror&#39;s outer surface. 
     Preferably, the surface section of the piezoelectric crystal completely covers the second mirror&#39;s outer surface—seen along the beam path of the photons leaving the cavity through the first mirror. 
     The piezoelectric crystal may be a piezoelectric crystal layer having a surface section that is mechanically coupled to the second mirror&#39;s outer surface, and a given layer thickness. The size of the surface section preferably increases and the layer thickness preferably decreases if the control voltage has a first polarity, and the size of the surface section preferably decreases and the thickness preferably increases if the control voltage has an opposite second polarity. 
     Preferably, an insulator is arranged between the piezoelectric crystal and the second mirror&#39;s outer surface, the insulator being configured to electrically insulate the piezoelectric crystal from the second mirror&#39;s outer surface and to forward the mechanical strain of the piezoelectric crystal to the cavity. 
     The cavity is preferably arranged on a front surface of a substrate and the piezoelectric crystal is preferably arranged on a back surface of the substrate. The substrate may be formed by an etch stop layer. Such an etch stop layer may have been placed on a preliminary substrate that is removed during the processing of the device. 
     An insulator may be arranged between the piezoelectric crystal and the back surface of the substrate, the insulator being configured to electrically insulate the piezoelectric crystal from the substrate and to forward the mechanical strain of the piezoelectric crystal though the substrate to the cavity. 
     The single-photon source may have a controller and a voltage source, which is connected to the piezoelectric crystal and controlled by the controller. The controller is preferably adapted to control the voltage of the voltage source such that the quantum dot&#39;s emission frequency corresponds to the longitudinal resonance frequency of the cavity. 
     The cavity preferably forms a cylinder, and the quantum dot is preferably arranged inside the cylindrical cavity. The base contour of the cylindrical cavity may be of any form. For instance, the base contour may be a circle, a square, a rectangle, an ellipse, etc. The first and second mirrors are preferably arranged at the upper and lower cylinder end faces of the cylindrical cavity. 
     The quantum dot is preferably arranged in or adjacent (below or above) a current aperture that focuses charge carriers onto the quantum dot. The current aperture may be formed by an insulating layer having an opening. The quantum dot is preferably arranged in or adjacent (below or above) this opening. The insulating layer is preferably arranged parallel to the first and second mirror. 
     The quantum dot is preferably comprised by an active layer which is parallel to the first and second mirror. In this way, the same kind of strain (laterally tensile and vertically compressive or laterally compressive and vertically tensile) may be easily induced to both the cavity and the quantum dot by applying strain to the second mirror&#39;s surface. The active layer is preferably also parallel to the insulating layer of the current aperture. 
     According to a further preferred embodiment, the cavity is cylindrical and forms a cylinder; the first and second mirrors are arranged at opposite cylinder end faces of the cylinder; the piezoelectric crystal is a piezoelectric crystal layer; and the quantum dot is comprised by an active layer which is parallel to the first and second mirror and the piezoelectric crystal layer. The quantum dot may be arranged in or adjacent to a current aperture that focuses charge carriers onto the quantum dot, the current aperture being formed by an insulating layer having an opening, and the quantum dot being arranged in or adjacent to the opening. The insulating layer may be arranged parallel to the first and second mirror, the active layer, and the piezoelectric crystal layer. 
     The invention also relates to a method of emitting single photons, particularly for use in quantum cryptography, using a single-photon source having a cavity and at least one quantum dot arranged therein, the method comprising the step of:
         applying a voltage to a piezoelectric crystal being arranged outside the cavity and mechanically coupled to the cavity,   wherein in response to said voltage the piezoelectric crystal applies either a laterally tensile and vertically compressive strain to the cavity and the quantum dot, or a laterally compressive and vertically tensile strain, depending on the control voltage&#39;s polarity, and thereby shifts the resonance frequency and the radiation frequency in opposite directions.       

     The laterally tensile and vertically compressive strain may reduce the distance between the first and second mirror, increase the cavity&#39;s resonance frequency, and decrease the strain-dependent radiation frequency. The laterally compressive and vertically tensile strain may increase the distance between the first and second mirror, decrease the cavity&#39;s resonance frequency, and increase the strain-dependent radiation frequency. The voltage applied to the piezoelectric crystal may be varied until the emission frequency corresponds to the longitudinal resonance frequency of the cavity. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In order that the manner in which the above-recited and other advantages of the invention are obtained will be readily understood, a more particular description of the invention briefly described above will be rendered by reference to specific embodiments thereof which are illustrated in the appended figures. Understanding that these figures depict only typical embodiments of the invention and are therefore not to be considered to be limiting of its scope, the invention will be described and explained with additional specificity and detail by the use of the accompanying drawings in which 
         FIG. 1  shows a first exemplary embodiment of a single photon emitter according to the present invention; 
         FIG. 2  shows the single photon emitter according to  FIG. 1  if an electric voltage is applied to the piezoelectric crystal; 
         FIG. 3  shows in an exemplary fashion the frequency characteristic of two cavities having different Q-factors; and 
         FIG. 4  shows a second exemplary embodiment of a single photon emitter according to the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The preferred embodiments of the present invention will be best understood by reference to the drawings, wherein identical or comparable parts are designated by the same reference signs throughout. 
     It will be readily understood that the present invention, as generally described herein, could vary in a wide range. Thus, the following more detailed description of the exemplary embodiments of the present invention, is not intended to limit the scope of the invention, as claimed, but is merely representative of presently preferred embodiments of the invention. 
       FIG. 1  shows a first exemplary embodiment of a single-photon source  10  according to the present invention. The single-photon source  10  comprises a cylindrical cavity  20  having a first mirror  30  and a second mirror  40 . The first mirror  30  and the second mirror  40  may be distributed Bragg reflectors DBR as indicted in an exemplary fashion in  FIG. 1 . The distributed Bragg reflectors DBR may consist of Al(Ga)O x -material. 
     The cavity  20  exhibits a plurality of longitudinal resonance frequencies between the first and second mirror  30  and  40 . The longitudinal resonance frequencies depend on the distance between both mirrors  30  and  40 . 
     At least one quantum dot  50  is formed in an active layer  55  and arranged inside the cavity  20 . The quantum dot  50  is positioned inside or adjacent (above or below) an opening  60  of a non-conductive layer  70 . The opening  60  is filled with conductive semiconductor material such as AlGaAs. The non-conductive layer  70  forms a current aperture through which electrical current may flow in vertical direction. The current aperture focuses the electrical current towards the single quantum dot  50  in order to increase the current efficiency and to avoid pumping of other (unused) quantum dots, which might be positioned in the active layer  55 . 
     The quantum dot  50  generates radiation at a specific radiation frequency when charge carriers (e.g. electrons and holes) are injected therein. The quantum dot  50  preferably consists of semiconductor material such as InGaAs material, and is thus very strain-dependent. As such, the radiation frequency of the emitted radiation is also very strain-dependent. 
     A charge carrier injection device is formed by a p-doped contact layer  90  and an n-doped contact layer  100 . If a positive voltage is applied to the contacts  110  and  120 , which are connected with both contact layers  90  and  100 , charge carriers are generated and injected into the cavity  20 . These charge carriers excite the quantum dot  50  to generate radiation in form of single photons P. The photons P are coupled out of the cavity  20  through the first mirror  30  if the emission frequency corresponds to the longitudinal resonance frequency of the cavity  20 . 
     The contacts  110  and  120  may be within the cavity or outside the mirrors. In  FIG. 1 , the contacts  110  and  120  are additionally marked as “p” and “n” since they contact the p-doped layer  90  and the n-doped layer  100 , respectively. 
     As can be seen in  FIG. 1 , the second mirror&#39;s outer surface  41  is arranged on the front surface  131  of a substrate  130 . A piezoelectric crystal  140  is arranged on the back surface  132  of the substrate  130 . The substrate  130  may consist of GaAs semiconductor material. 
     The piezoelectric crystal  140 , which may consist of PMN-PT (lead magnesium niobate-lead titanate Pb(Mg 1/3 Nb 2/3 )O 3 —PbTiO 3 ) material, is electrically connected to a controllable voltage source  150  which is controlled by a controller  160 . 
     The piezoelectric crystal  140  is mechanically coupled to the second mirror&#39;s outer surface  41  through the substrate  130 . As such, the piezoelectric crystal  140  may apply either a laterally tensile and vertically compressive strain to the cavity  20  and the quantum dot  50  inside the cavity  20 , or a laterally compressive and vertically tensile strain. The kind of strain depends on the control voltage&#39;s polarity. Therefore, the controller  160  may influence and control the emission behavior of the quantum dot  50  and the resonance frequency of the cavity  20  by applying an appropriate control voltage. 
     In order to efficiently transfer the mechanical stress induced by the piezoelectric crystal  140  into the cavity  20 , the upper surface of the piezoelectric crystal  140  is preferably larger than the second mirror&#39;s outer surface  41  and preferably interacts with the entire second mirror&#39;s outer surface  41 . 
     The active layer  55  is preferably arranged parallel to the first and second mirror  30  and  40 . As such, the same kind of strain (laterally tensile and vertically compressive or laterally compressive and vertically tensile) is induced to both the cavity and the quantum dot when strain is induced to the second mirror&#39;s surface  41 . 
     As discussed above, the embodiment shown in  FIG. 1  comprises a substrate  130  which separates the piezoelectric crystal  140  from the second mirror&#39;s outer surface. In order to provide efficient transfer of mechanical strain from the piezoelectric crystal  140  to the second mirror  40 , the quantum dot  50  and the first mirror  30 , the thickness of substrate  130  should be as small as possible, or the substrate  130  should be omitted, if possible. 
     For instance, the substrate  130  as shown in  FIG. 1 , may be formed by an etch stop layer which was formerly placed on top of a preliminary substrate (not shown in  FIG. 1 ) during the fabrication of the second mirror  40 , the quantum dot  50  and the first mirror  30 . During said fabrication, the second mirror  40 , the quantum dot  50  and the first mirror  30  may be deposited on the etch stop layer which is placed on top of the preliminary substrate. Afterwards, the preliminary substrate is removed, for instance by etching. The remaining structure composed of the second mirror  40 , the quantum dot  50 , the first mirror  30 , and the etch stop layer may then be equipped with the piezoelectric crystal  140 . 
     In the embodiment shown in  FIG. 1 , the cavity is oriented along and photon emission occurs in the vertical direction “z”. A lateral direction is any direction (e.g. “x” and “y”) that is perpendicular to the vertical direction “z” along which the cavity is oriented and photons are emitted. A lateral direction is a direction in 3-dimensional space that is perpendicular to the vertical direction “z”. 
       FIG. 2  shows the embodiment of  FIG. 1  during operation. In the middle section of  FIG. 2 , the voltage V piezo  is zero and no strain is applied to the cavity  20  or the quantum dot  50 . In the following, it is assumed that the radiation frequency f QD  of the photons generated by the quantum dot  50  does not match with the resonance frequency f cav  of the cavity  20  at a given temperature T 1 . As such the photon energy E QD =h*f QD  does not equal the resonance energy E cav =h*f cav  either. 
     Depending on the cavity&#39;s quality factor, there is no efficient emission of photons P when the emission frequency of the radiation does not lie in the spectral transmission window of the cavity  20 . This is shown in  FIGS. 3   a  and  3   b  by two examples. The cavity&#39;s quality factor is indicated by the reflection characteristics R of the cavity  20 . 
     In  FIG. 3   a , the cavity&#39;s quality factor is small and the radiation I is emitted even though the radiation frequency f QD  does not perfectly match the cavity dip, i.e. the resonance frequency f cav  of the cavity  20 . In  FIG. 3   b , the cavity&#39;s quality factor is better and the radiation I is not emitted since the radiation frequency f QD  does not match the resonance frequency f cav  of the cavity  20 . In order to increase ( FIG. 3   a ) or enable ( FIG. 3   b ) an efficient emission of radiation the radiation frequency f QD  and the resonance frequency f cav  need to be shifted relative to each other as indicated by reference numeral I′ in  FIGS. 3   a  and  3   b.    
     Referring again to  FIG. 2 , one can see that by applying a positive voltage V piezo  to the piezoelectric crystal  140  at the temperature T 1 , a laterally compressive and vertically tensile strain is induced in the piezoelectric crystal  140 , the cavity  20 , and the quantum dot  50 . The thickness of the piezoelectric crystal  140  increases from a thickness d (V piezo =0) to a larger thickness d′ (V piezo &gt;0), and the surface A of the piezoelectric crystal  140  decreases from a value A (V piezo =0) to a reduced value A′ (V piezo &gt;0). This mechanical deformation has an impact on the cavity  20  and the quantum dot  50 . The distance H between both mirrors  30  and  40  increases, and the resonance frequency f cav  and the resonance energy E cav  decrease. Due to the deformation of the quantum dot  50 , the photon energy E QD Of the quantum dot  50  increases. As such, applying a positive voltage V piezo  does not increase the radiation efficiency since E cav  and E QD  further separate from each other. 
     However, by applying a negative voltage V piezo  to the piezoelectric crystal  140  at the temperature T 1 , the radiation efficiency will be increased. A negative voltage V piezo  induces a laterally tensile and vertically compressive strain in the piezoelectric crystal  140 , the cavity  20 , and the quantum dot  50 . It can be seen in  FIG. 2  that the thickness of the piezoelectric crystal  140  decreases from a thickness d (V piezo =0) to a smaller thickness d″ (V piezo &lt;0), and the surface A of the piezoelectric crystal  140  increases from a value A (V piezo =0) to a larger value A″ (V piezo &lt;0). Again, this mechanical deformation has an impact on the cavity  20  and the quantum dot  50 . The distance H between both mirrors  30  and  40  decreases, and the resonance frequency f cav  and the resonance energy E cav  increase. Due to the deformation of the quantum dot  50 , the photon energy E QD  decreases. By applying the appropriate negative voltage V piezo , E cav  and E QD  may be brought to a perfect match. 
     If the temperature increases from T 1  to T 2 , E cav  increases and E QD  decreases, and the radiation efficiency will drop. This negative effect can be compensated by applying a different voltage as shown in  FIG. 2 . In case of a positive voltage V piezo , E cav  and E QD  will be shifted together and a perfect match may be also achieved at the temperature T 2 . 
     In order to control the voltage V piezo  that is applied by the voltage source  150 , the controller  160  may be connected to a detector which detects the photons P emitted through the first mirror  30 . For instance, a feed-back loop may be provided which controls the voltage V piezo  in order to keep E cav  and E QD  matched and the photon emission at its maximum level. 
       FIG. 4  shows a second exemplary embodiment of a single-photon source  10  according to the present invention. 
     In contrast to the first embodiment, an insulating layer  170  is disposed between the substrate  130  and the piezoelectric crystal  140 . 
     
       
         
               
             
               
               
               
             
           
               
                   
               
               
                 Reference signs 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 10 
                 single-photon source 
               
               
                   
                 20 
                 cavity 
               
               
                   
                 30 
                 first mirror 
               
               
                   
                 40 
                 second mirror 
               
               
                   
                 41 
                 second mirror&#39;s outer surface 
               
               
                   
                 50 
                 quantum dot 
               
               
                   
                 55 
                 active layer 
               
               
                   
                 60 
                 opening 
               
               
                   
                 70 
                 non-conductive layer 
               
               
                   
                 90 
                 p-doped contact layer 
               
               
                   
                 100 
                 n-doped contact layer 
               
               
                   
                 110 
                 contact to p-doped layer 90 
               
               
                   
                 120 
                 contact to n-doped layer 100 
               
               
                   
                 130 
                 substrate 
               
               
                   
                 131 
                 front surface 
               
               
                   
                 132 
                 back surface 
               
               
                   
                 140 
                 piezoelectric crystal 
               
               
                   
                 150 
                 controllable voltage source 
               
               
                   
                 160 
                 controller 
               
               
                   
                 170 
                 insulating layer 
               
               
                   
                 A 
                 surface 
               
               
                   
                 A′ 
                 surface 
               
               
                   
                 A″ 
                 surface 
               
               
                   
                 d 
                 thickness 
               
               
                   
                 d′ 
                 thickness 
               
               
                   
                 d″ 
                 thickness 
               
               
                   
                 f cav   
                 resonance frequency 
               
               
                   
                 f QD   
                 radiation frequency 
               
               
                   
                 E cav   
                 resonance energy 
               
               
                   
                 E QD   
                 photon energy 
               
               
                   
                 H 
                 distance 
               
               
                   
                 H′ 
                 distance 
               
               
                   
                 H″ 
                 distance 
               
               
                   
                 I 
                 radiation 
               
               
                   
                 I′ 
                 radiation 
               
               
                   
                 P 
                 Photon 
               
               
                   
                 R 
                 reflection characteristic 
               
               
                   
                 T1 
                 temperature 
               
               
                   
                 T2 
                 temperature 
               
               
                   
                 V piezo   
                 voltage