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A quantum logic gate between a solid-statequantum bit and a photonHyochul Kim1, Ranojoy Bose1, Thomas C. Shen1, Glenn S. Solomon2 and Edo Waks1,2*

Integrated nanophotonic devices create strong light–matterinteractions that are important for the development of solid-state quantum networks1, distributed quantum computers2

and ultralow-power optoelectronics3,4. A key component formany of these applications is the photonic quantum logicgate, where the quantum state of a solid-state quantum bit(qubit) conditionally controls the state of a photonic qubit.These gates are crucial for the development of robustquantum networks5–7, non-destructive quantum measure-ments8,9 and strong photon–photon interactions10. Here, weexperimentally realize a quantum logic gate between anoptical photon and a solid-state qubit. The qubit is composedof a quantum dot strongly coupled to a nanocavity, which actsas a coherently controllable qubit system that conditionallyflips the polarization of a photon on picosecond timescales,implementing a controlled-NOT gate. Our results represent animportant step towards solid-state quantum networks andprovide a versatile approach for probing quantum dot–photoninteractions on ultrafast timescales.

Quantum dots are semiconductor emitters that can storequantum information using both excitons11 and spin12–16. Becausethey are embedded in a host material, these solid-state qubits canbe practically integrated into photonic devices without complexatomic traps. They can also mediate two-qubit quantum operationsbetween distinguishable excitons confined in a single dot17, as wellas between two spins in vertically coupled dots18.

In a quantum network, quantum dots must strongly interact withphotonic qubits to create and distribute entanglement. Severalworks have proposed using optical nanocavities to implementthese interactions by direct quantum logic gates5–7. These gatesexploit the strong coupling regime of cavity quantum electro-dynamics19–22, where a single quantum dot can greatly alter thenanocavity spectral response23,24.

We realize a quantum logic gate using an InAs quantum dotstrongly coupled to a photonic crystal cavity. Figure 1a illustratesthe quantum-dot level structure, which includes a ground state |gland two bright exciton states, labelled |þl and |2l, representingthe two anti-aligned spin configurations of the electron and hole.The optical transitions from the ground state to the two bright exci-tons, denoted sþ and s2 , exhibit right- and left-circularly polarizedemission, respectively, at high magnetic fields. A magnetic field inthe sample growth direction (Faraday configuration) tunes the sþtransition on resonance with the cavity while simultaneously detun-ing the s2 transition25. In this configuration, states |gl and |2l arethe qubit states of the quantum dot, and the sþ transition couplesthe qubit to a photon. The cavity serves the dual role of creating aphotonic interface through cavity reflectivity modification23,24 viathe sþ transition, and suppressing the spontaneous emission ofthe s2 transition.

Figure 1b presents a scanning electron microscopy (SEM) imageof the fabricated photonic crystal cavity (see Methods andSupplementary Section S1 for details on device design and fabrica-tion). These cavities exhibit high-Q modes that have a well-definedpolarization. The photonic qubit encodes quantum informationusing the polarization states |Hl and |Vl rotated 458 relative to thepolarization axis of the cavity. The qubit states can be expressedin the polarization basis that is parallel and orthogonal to thecavity axis, denoted |xl and |yl respectively, using the relations|Hl¼ (|xlþ |yl)/

��

2√

and |Vl¼ (|yl 2 |xl)/��

2√

. Upon reflectionfrom the sample surface, the photonic qubit states will be trans-formed to the states |Hl � (r|xlþ |yl)/

��

2√

and |Vl � (|yl 2

r|xl)/��

2√

where r is the cavity reflection coefficient. This reflectioncoefficient can be directly calculated from the Heisenberg–Langevin equations of motion (Supplementary Section S2). If thephoton is resonant with the cavity mode and the quantum dot isin state |2l (Fig. 1c, bottom), the system behaves like a barecavity and r¼21. The photonic qubit therefore experiences a bitflip (|Hl �|Vl and |Vl �|Hl). If, however, the quantum dot isin state |gl (Fig. 1c, top), the optical transition to the |þl state willstrongly modify the reflection coefficient23,24. When both thephoton and the sþ transition are resonant with the cavity, thereflection coefficient becomes r¼ (C 2 1)/(Cþ 1), where C¼2g2/gk is the atomic cooperativity. The parameters g, k and gdenote the cavity–quantum dot coupling strength, cavity energydecay rate and exciton decay rate for the sþ transition, respectively.In the limit C ≫ 1, r � 1 and the photonic qubit remainsunchanged (|Hl �|Hl and |Vl �|Vl). Thus, the state of thequantum dot controls whether the photonic qubit will experiencea bit flip, which implements a complete controlled-NOT (cNOT)logic gate.

We initially characterized the device under continuous-wave(c.w.) excitation using a broadband light-emitting diode (LED; seeMethods). Figure 2a plots the cavity reflection spectrum as a func-tion of magnetic field, with the cavity excited using a verticallypolarized input field and the reflected intensity measured alongthe horizontally polarized component. At 0 T, the spectrumshows a bright peak due to the cavity, and a second peak due tothe quantum dot that is blue-detuned from the cavity resonanceby 0.11 nm. As we increase the magnetic field the quantum dotline splits into two peaks corresponding to the sþ transition (red-shift) and the s2 transition (blueshift). The sþ transition exhibitsan anti-crossing when tuned across the cavity resonance, whichindicates the system operates in the strong coupling regime.Figure 2b presents a high-spectral-resolution measurement per-formed using a tunable narrowband laser at 1.6 T (see Methods),when the sþ transition is resonant with the cavity, together witha numerical fit to a theoretical model (Supplementary Section S3).From the numerical fit we determine g/2p¼ 12.9 GHz and

1Department of Electrical and Computer Engineering, IREAP, University of Maryland, College Park and Joint Quantum Institute, University of Maryland,College Park, Maryland 20742, USA, 2Joint Quantum Institute, National Institute of Standards and Technology, and University of Maryland, Gaithersburg,Maryland 20899, USA. *e-mail: edowaks@umd.edu

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ΔE

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Figure 1 | Implementation of a quantum dot–photon cNOT operation. a, Energy level structure of a neutral quantum dot (QD) under a magnetic field. b,

SEM image of the fabricated device and the cavity axis relative to photon polarization. c, Illustration of cNOT operation. The polarization of an incident photon

is preserved when the quantum dot is in state |gl (top), and is rotated when the quantum dot is in state |2l (bottom). The horizontal dashed lines indicate

the degenerate energy level of the |þl quantum dot state and the cavity photon state, which are split into two polariton states |Pþl and |P2l in the strong

coupling regime. d, Measurement set-up. Pump and probe polarization is selected and measured using a PBS and a HWP. A flip mirror (FM) is used to direct

the probe signal from either the transmitted or reflected port of the PBS to a single-mode fibre (SMF) and then to a grating spectrometer. OL, objective lens;

BS, beam splitter; M, mirror; QD, quantum dot.In

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Figure 2 | Device characterizations under c.w. excitation. a, Cavity spectrum measured using a broadband LED as a function of magnetic field at a

temperature of 4.3 K. b, Cavity spectrum measured using a tunable narrowband diode laser at a magnetic field of 1.6 T. The red solid line is a fit to a

theoretical model. c, Cavity spectrum measured using a broadband LED as a function of diode laser frequency, which is swept across the s2 transition

of the quantum dot (QD) at a magnetic field of 1.6 T. When the pump laser is resonant with the s2 transition, the dip induced by the quantum dot is

inhibited. d–f, Cavity spectra for pump laser detunings of DL/2p¼ 10, 0 and 210 GHz, respectively, relative to the s2 transition.

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k/2p¼ 31.9 GHz (Quality factor Q¼ 10,200). The measuredvalues of g and k satisfy the strong coupling condition g . k/4,proving that the device operates in the strong coupling regime19–24.

To populate the |2l state, we excited the sample with a tunablenarrowband laser while simultaneously probing the cavityspectrum with the broadband LED. Figure 2c shows the spectrumas a function of detuning between the tunable laser and thes2 transition (DL/2p) using a pump power of 1.8 mW (measuredbefore the objective lens). When the pump laser is resonant withthe s2 transition it creates a strong modification of the cavityspectrum. Figure 2d–f plots the measured spectrum for specificlaser detunings of 10, 0 and 210 GHz, respectively. At 0 GHzdetuning, the central dip in the cavity spectrum is suppressedbecause the quantum dot is incoherently pumped into the |2lstate. This suppression quickly vanishes at both red- and blue-detuned pump wavelengths.

To demonstrate quantum gate operation, we used short opticalpulses to prepare the initial qubit state of the quantum dot and gen-erate the photonic qubit. A 10 ps pump pulse resonant with the s2

transition prepared the state of the quantum dot through coherentRabi oscillations, while an attenuated 75 ps probe pulse served asthe photonic qubit (see Methods). We selected these pulse durationsto be short compared to the lifetime of the |2l state (SupplementarySection S4), and also to ensure that the probe pulse spectrum wasnarrower than the spectral dip in Fig. 2b.

Figure 3a plots the probe intensity as a function of the squareroot of the average pump power P, where we set the incidentprobe pulse to be vertically polarized and measured the reflectedpulse along the horizontal polarization axis. The figure displaysthe results for both 80 ps and 4 ns pump–probe delays. The datareveal a clear oscillatory behaviour for 80 ps delay due to Rabi oscil-lation between states |gl and |2l, where a pump power of 0.12 mWachieves a p-pulse. These oscillations vanish at 4 ns delay becausethe quantum dot has decayed back to the ground state before thephotonic qubit interacts with the cavity. The contrast of the Rabioscillations degrades with increasing pump intensity, an effect thatwe attribute to phonon-mediated excitation-induced dephasing26,27.

To obtain the full time-resolved reflection spectrum, we tunedthe probe beam frequency across the cavity resonance. Figure 3b–e shows the measured probe intensity for 0, p, 2p and 3p pumppulse amplitudes for both 80 ps and 4 ns delays, together withtheoretical fits. At 80 ps delay, the spectrum oscillates betweenthe bare cavity lineshape and the lineshape of a stronglycoupled cavity–quantum dot system. The blue solid curves inFig. 3c and e represent the ideal bare cavity spectra when thequantum dot is excited to the |2l state with unity probability.In Fig. 3c, the measured signal at 80 ps delay for the cavity res-onant wavelength (920.97 nm) achieves 95% of the maximumpredicted value. From this value we calculate the occupation prob-ability of the |2l state to be 0.93+0.04 after a p pulse(Supplementary Section S5). We attribute the small reductionfrom unity probability to the spontaneous decay of the |2lstate that may occur before the photonic qubit has finished inter-acting with the cavity.

Figure 4 shows pump–probe measurements for the four possiblecombinations of input and output photon polarizations (seeMethods). We tuned the probe beam frequency across the cavity res-onance while pumping the s2 transition with a p pulse.Measurements taken at 80 ps delay correspond to a quantum dotin the |2l state with high probability, while at 4 ns delay thequantum dot has decayed back to state |gl. In Fig. 4a we set the inci-dent polarization to be vertically polarized, as in Fig. 3c, butmeasured the probe intensity along the vertical polarization axisinstead. In this case we observed the reverse behaviour, where aquantum dot in state |2l produces a minimum measured intensityat the cavity resonant wavelength, while a quantum dot in state |glcreates a maximum. Figure 4b–d plots the remaining combinationsof input and output polarizations.

Optimal gate operation is attained when the input field is res-onant with the quantum dot sþ transition (920.96 nm). Figure 4eshows the probability table for the quantum gate under this operat-ing condition (Supplementary Section S6). When the quantum dotis in state |2l, the probabilities of a bit flip are PH�V¼ 0.93+0.03and PV�H¼ 0.98+0.04, giving the gate fidelity (the probability ofbeing in the correct output state) for the two input polarizations.When the quantum dot is in state |gl, the gate fidelities are givenby PV�V¼ 0.58+0.04 and PH�H¼ 0.61+0.07. The reduction ingate fidelity in this case is due to finite cooperativity and spectralwandering, consistent with the contrast measured in Fig. 2b undermonochromatic excitation.

In conclusion, we have demonstrated a quantum gate between aquantum dot and a photon, an important enabler for robust and

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Figure 3 | Demonstration of controlled bit flip by pulsed pump–probe

excitation. a, Plot of the change in measured intensity of the probe signal

along the H-polarization direction as a function of the square root of average

pump power at 80 ps (blue circles) and 4 ns (red squares) pump–probe

delay time. The probe beam wavelength is resonant with the cavity

(920.97 nm). b–e, Probe signal intensity (H-polarized) as a function of

excitation wavelength at 0 (b), p (c), 2p (d) and 3p (e) pumping

conditions. Blue circles, 80 ps delay; red squares, 4 ns delay. Solid lines are

fits to a theoretical model.

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scalable quantum networks5–7, and the generation of strongphoton–photon interactions10. The switching contrast and gatespeed could be improved by using photonic crystal cavity designswith smaller mode volumes28, and by better alignment of thequantum dot with the high-field mode of the cavity22. Theseresults can also be extended to qubits based on electron and holespins of charged quantum dots, which exhibit significantly longercoherence times12–16,18. The current device implementation can beadapted to a planar integrated architecture by using a waveguide-coupled cavity–quantum dot system29. When combined with localquantum dot tuning methods30, these devices provide a potentialroute towards quantum information processing on a chip.

MethodsDevice fabrication. The sample consisted of a 160 nm GaAs layer on top of a 1 mmAlGaAs sacrificial layer grown by molecular beam epitaxy. A single layer of self-assembled InAs quantum dots (density of 10–50 mm22) was grown in the centre ofthe GaAs layer. A distributed Bragg reflector composed of 10 layers of GaAs andAlAs was grown below the photonic crystal layer and acted as a high reflectivitymirror, enabling the device to behave as a one-sided cavity23. Photonic crystalcavities with a three-hole defect (L3 cavity) were fabricated using electron beamlithography, followed by Cl2-based dry etching, and finally wet-etch removal of theAlGaAs sacrificial layer using hydrofluoric acid.

Measurement set-up. The sample was mounted in a continuous-flow liquid-heliumcryostat and cooled to 4.3 K. The sample mount was surrounded by asuperconducting magnet able to apply magnetic fields of up to 7 T. Sampleexcitation and collection were performed by confocal microscopy using an objectivelens with a numerical aperture of 0.68. The polarization axis for excitation andcollection was set by a half-wave plate (HWP) and analysed by a polarizingbeamsplitter (PBS), as illustrated in Fig. 1d. The collected signal was focused into asingle-mode fibre to spatially filter only the cavity-coupled signal and isolate a singletransverse mode, and then measured by a grating spectrometer and nitrogen-cooled

charge-coupled device (CCD) camera. The resolution of the spectrometer camerasystem was 7 GHz.

Continuous-wave measurement. The cavity spectrum was measured using either abroadband LED or a tunable diode laser. The LED was used as a white light sourcewith dominant emission in the wavelength range 900–950 nm. The diode laser had anarrow linewidth (.300 kHz) that could be continuously tuned between 920 and940 nm. The high-resolution cavity spectrum in Fig. 2b was measured bycontinuously sweeping the tunable laser frequency over the cavity resonance andmeasuring the reflected laser signal. Each data point in Fig. 2b was obtained byfitting the measured laser signal with a Gaussian function, where the frequency andscattering intensity of each data point were obtained from the Gaussian fit.Figure 2c–f was obtained by sweeping a diode laser frequency over the s2 transitionto pump the |2l state, while simultaneously probing the cavity spectrum with thebroadband LED. Background noise due to inelastic scattering from the pump wassubtracted in Fig. 2d–f. The contrast of the dip induced by the quantum dot inFig. 2d and f was measured to be 25% on resonance with the sþ transition, whichwas lower than the measured contrast in Fig. 2b due to limited spectrometerresolution as well as off-resonant excitation of the sþ transition by the pump laser.

Pump–probe pulse measurement. The pump and probe were generated using twotime-synchronized Ti:sapphire lasers. The sample was maintained at 4.3 K, and amagnetic field of 3–5 T was applied depending on the detuning between thequantum dot and the cavity. The lasers were synchronized by piezo feedback in theprobe laser cavity, which locked its clock frequency to the pump laser with anaccuracy of 100 fs. The delay between the pump and probe was controlledelectronically by a phase-lock loop in the synchronization electronics. The pumppulse duration, initially 2 ps, was expanded to 10 ps by spectral filtering, and theprobe pulse duration, initially 5 ps, was filtered to 75 ps using separate gratingspectrometers. After filtering, the probe beam passed through an intensity stabilizer.The pump–probe delay was measured by a single-photon avalanche photodiodewith 30 ps resolution. The probe beam power was set to 1 nW, measured before theobjective lens. The coupling efficiency of the probe into the cavity mode has beenmeasured previously to be 0.16% (ref. 31). This efficiency, together with the laserrepetition rate of 76 MHz, indicates that the mean number of probe photons perpulse coupled to the cavity was 0.1. In addition to the probe signal detected in theCCD, an inelastic scattering of the pump was observed. This background, measured

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Figure 4 | cNOT operations for all four combinations of input–output polarizations. a–d, Cavity spectra are measured with a p-pulse pump for 80 ps (blue

circles) and 4 ns (red squares) pump–probe delay using the four possible combinations of input polarization |alin and measured polarization |blout, where a,b

[ [H, V]. Solid lines are fits to a theoretical model. e, Measured probability Pa�b at 80 ps pump–probe delay when a quantum dot is pumped to state |2l by

a p-pulse (top) and at 4 ns delay when it has relaxed back to state |gl (bottom). QD, quantum dot.

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to be �5% at the p pulse condition and increasing to 14% at the 3p pulse condition,was subtracted for Fig. 3.

Measurement of complete input–output photon polarization probabilities. AHWP placed between the PBS and the objective lens was used to rotate the inputphoton polarization to either H or V. After reflection, the photon underwent asecond pass through the HWP due to the optical configuration of the set-up. Whenthe HWP was oriented at 08, a detection event from the transmitted port of the PBScorresponded to a photon polarized in the H direction after reflection, while adetection event from the reflected port corresponded to V polarization. In contrast,when the HWP was rotated 458, a detection event at the transmission port of the PBScorresponded to a V-polarized photon after reflection from the cavity, while thereflection port corresponded to an H-polarized photon. This additional rotation wastaken into account in the data in Fig. 4a and d.

Received 18 September 2012; accepted 8 February 2013;published online 31 March 2013

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AcknowledgementsThe authors acknowledge support from the Army Research Office MultidisciplinaryUniversity Research Initiative on hybrid quantum interactions (grant no. W911NF09104),a Defense Advanced Research Projects Agency (DARPA) Defense Science Office grant(grant no. W31P4Q0910013), the Physics Frontier Center at the Joint Quantum Institute,and the Office of Naval Research Applied Electromagnetics Center. E.W. acknowledgessupport from the National Science Foundation Faculty Early Career Development(CAREER) award (grant no. ECCS 0846494) and a DARPA Young Faculty Award (grantno. N660011114121).

Author contributionsH.K. and E.W. conceived and designed the experiment, and prepared the manuscript. H.K.carried out the measurements and analysed the data. R.B. and T.C.S. contributed to themeasurements and sample design. E.W. and H.K. carried out the theoretical analysis. G.S.S.provided samples grown by molecular beam epitaxy.

Additional informationSupplementary information is available in the online version of the paper. Reprints andpermissions information is available online at www.nature.com/reprints. Correspondence andrequests for materials should be addressed to E.W.

Competing financial interestsThe authors declare no competing financial interests.

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