Efficient deterministic giant photon phase shift from a single charged quantum dot
P. Androvitsaneas, A. B. Young, J.M. Lennon, C. Schneider, S. Maier, J.J. Hinchliff, G. Atkinson, M. Kamp, S. Höfling, J. G. Rarity, R. Oulton
EEfficient deterministic giant photon phase shift from a single charged quantum dot
P. Androvitsaneas, A. B. Young, J.M. Lennon, C. Schneider, S. Maier, J.J. Hinchliff,
1, 3
G.S. Atkinson, E. Harbord, M. Kamp, S. H¨ofling,
2, 4
J. G. Rarity, and R. Oulton Quantum Engineering Technology Labs, H. H. Wills Physics Laboratory andDepartment of Electrical & Electronic Engineering, University of Bristol, BS8 1FD, UK Technische Physik, Physikalisches Institut and Wilhelm Conrad R¨ontgen-Center for Complex Material Systems,Universit¨at W¨urzburg, Am Hubland, 97474 W¨urzburg, Germany Quantum Engineering Centre for Doctoral Training,H. H. Wills Physics Laboratory and Department of Electrical and Electronic Engineering,University of Bristol, Tyndall Avenue, BS8 1FD, United Kingdom SUPA, School of Physics and Astronomy, University of St Andrews, St Andrews, KY16 9SS, United Kingdom
Solid-state quantum emitters have long been recognised as the ideal platform to realize integrated quantumphotonic technologies. We use a self-assembled negatively charged QD in a low Q-factor photonic micropillarto demonstrate for the first time a key figure of merit for deterministic switching and spin-photon entanglement:a shift in phase of an input single photon of > o with values of up to π/ ( o ) demonstrated. This > π/ ( o ) measured value represents an important threshold: above this value input photons interact withthe emitter deterministically. A deterministic photon-emitter interaction is the only viable scalable means toachieve several vital functionalities not possible in linear optics such as quantum switches and entanglementgates. Our experimentally determined value is limited by mode mismatch between the input laser and thecavity, QD spectral fluctuations and spin relaxation. We determine that up to of the collected photons haveinteracted with the QD and undergone a phase shift of π . The dramatic progress made in quantum dots (QD) hasled to single photon sources with record efficiency andindistinguishability [1–4].However, QDs are not just ex-ploited as sources; by maximising the interaction of the QDwith light, one may use the QD transition to determinis-tically “switch” the phase, φ , of a single photon by up to π . Here we present the first solid-state implementation thatachieves this key figure of merit. Using a low quality fac-tor (Q-factor) micropillar in the “bad-cavity” limit we mea-sure a phase shift of at least π/ ( ◦ ). Accounting forbackground (20%), this corresponds to a π phase shift of allthe photons reflected from the QD-cavity system. By com-bining this with the selection rules for QD spin transitions,one may unlock the ability to perform efficient, high fidelityquantum entanglement operations [5–9].There are two overarching requirements for designing apractical quantum photonic switch: firstly the passive pho-tonic structure must possess well-defined and input andoutput modes facilitating efficient optical coupling. Sec-ondly the quantum emitter should show perfect interaction(i.e. π phase shift for every interacting photon) and mini-mal photon scattering into leaky modes ( γ ) rather than theinput/output mode ( Γ ), i.e. a high β -factor ( β = ΓΓ+ γ ).Such conditions have been satisfied using atom-cavity sys-tems [10–13], but this has so far remained elusive for solidstate quantum emitters, a more natural platform for inte-grable/scalable devices. In this manuscript we present anovel approach using a low Q-factor micropillar cavity of-ten termed the “bad cavity” limit [14]. By doing this weensure a well-defined, efficient input and output mode [15],in contrast to more traditional approaches using high Q- factor cavities [16, 17] where limits in current fabricationtolerances lead to scattering into parasitic modes, limitingthe phase shift to the order of ∼ π/ [18–20]. Recentdemonstrations have exploited a similar small photon phaseshift to probabilistically herald a π phase switch on the QDspin, upon the successful detection of a rotated photon [21].Importantly, in that case one needed to post-select on ro-tated photons, which occurs with a low probability. We nowdemonstrate the next step, showing instead a phase switchimparted by the QD onto the photons in a deterministicmanner (i.e. all photons that have interacted with the QDundergo a phase shift of π ). A deterministic interaction isessential in order to build large chains of entangled photonsfor cluster state quantum computation [22, 23].A both bright and deterministic device is made possibleby the unique properties of the low Q-factor micropillardesign ( Q ∼ ) which inherently has negligible pas-sive losses. Further, we have already demonstrated [24]that these low Q-factor cavities also have a high β -factor( β ∼ . with up to β > . possible), and therefore thesestructures currently represent the state of the art in terms ofa practical solid-state quantum photonic switch. Our previ-ous work [24] has shown phase shifts ∼ ◦ , whilst we cal-culate that this QD-micropillar should give a π phase shiftfor resonantly reflected photons (see supplement). The lowphase shift actually measured in Ref. [24] is largely dueto spectral “jitter” which leads to a shift ( δω ) in the spec-tral position of the QD over a timescale shorter than thelaser scan time [25]. In those experiments with one sec-ond integration times we probe a range of QD laser detun-ings ( δω ), which gives rise to a much lower average photon a r X i v : . [ qu a n t - ph ] M a y PBS PBS APD 1 (V)
SBLP
Single+frequency+tunable+laserOff+resonant+laser
BS4K+Cryostat Permanent+ring+magnetBS
APD 2 (H)APD 4 (H)APD 3 (V) (a)
Coherent+Scattering σ σ - + Δ E=40 μ eV (b) FIG. 1: ( a ). Experimental setup used to time resolve the QD in-duced phase shift. A
50 : 50 beamsplitter (BS) splits the reflectedsignal into two channels. One which sends photons to APD-1 andAPD-2 that are used as heralding detectors, with the independentlycorrelated phase shift measured via APD-3 and APD-4. ( b ) En-ergy level diagram of a negatively charged QD in a Faraday mag-netic field. Measurements are performed on light that is resonantlyscattered from the spin down transition. phase shift.In this work we overcome the spectral jitter by measur-ing the photon phase shift in µ s intervals (faster thanthe spectral jitter time). By using a specially designedtwo-channel heralding technique, we explore time windowswhen the QD remains close to resonance with the laser,and measure the phase shift of light reflected from theQD-micropillar system. This is possible due to the highbrightness of the system (large β -factor, and low passivecavity losses), where we can on average detect on the or-der of 100 photons in 100 µ s, even in the weak excitationlimit. We consistently evaluate phase shift values > π/ when the QD is close to resonance ( | δω | < Γ / ) where Γ is the linewidth of the transition. We also demonstratethat in the rare cases where the laser remains precisely on-resonance ( | δω | < Γ / ), we measure phase shifts of upto π/ ± π/ . Note that resonant phase shift values π/ < φ < π should not occur (see supplementary), andso measurement of φ > π/ reveals that the determinis-tic regime ( φ = π ) has already been reached, but that theobservable phase shift is limited/obscured by backgroundnon-interating photons (20% of the collected signal).The experimental setup is shown in Fig.1.(a), verticallylinearly polarized coherent light | V (cid:105) from a single fre-quency laser is input to the micropillar, and spectrally tunedto the spin | ↓(cid:105) transition (see Fig.1.(b)). The reflectedsignal is split into two with a non-polarizing beamsplit-ter (BS1): one arm is sent to APDs 3 (vertical- V ) and 4(horizontal- H ); the other arm is sent to independent detec-tors that also measure in the linearly polarised basis APD-1( V ), APD-2 ( H ) (see methods). A lower bound value forthe phase shift ( cos ( φ LB ) ) that does not take into accountellipticity (see Supplementary for full details) and underes- Number of bins
C r o s s p o l a r i s e d r a t e A P D - 2 ( k H z ) f LB ( p ) FIG. 2: Frequency plot of the count rates in APD2 (cross po-larised) as measured in 100 µ s bins (black curve) left axis. Redcurve: displays the corresponding lower bound phase shift (rightaxis) measured by Eq.1 using APD-4 (H polarised) and APD-3 (Vpolarised) timates the phase can be calculated via: cos ( φ LB ) = V − HV + H (1)Cross-polarized counts are only observed when the laseris on-resonance with the QD and undergoes a Faraday ro-tation with a non-zero projection onto H. In non-cavity ex-periments this is the channel where cross-polarised reso-nant scattering is detected [25]. Initially we monitor thenumber of counts in the cross-polarised channel via APD-2. Fig.2 shows a histogram for the distribution of count-rates in APD-2 for µ s bin widths (note the logarithmicscale). The vast majority of time bins contain low count-rates of around 17kHz. This corresponds to the QD transi-tion shifted away from resonance with the input laser due tospectral jitter. Nevertheless there are still instances wherethe count-rate can become significantly higher. This in-crease represents light resonantly scattering from the QDtransition into the cross-polarised channel.It is particularly illuminating to correlate these count-rates with the phase measured according to Eq. 1 usingAPD-3 (V) and APD-4 (H). Using these detectors in a sep-arate arm allows us to obtain a measure of the phase shiftthat is correlated to APD-2, but that does not unfairly biasthe data we use to measure the phase shift. We expectthat when the cross-polarized count-rates in the heraldingarm are high, the phase shift of input photons will also besignificant. In Fig.2 we can clearly see that as the num-ber of cross-polarised counts increases so does the mea-sured phase shift, as expected. This reaches a peak value of φ LB = 0 . π ± . π at APD-2 count-rate 240kHz. Themeasured phase shift is limited by the heralding accuracy.At 240kHz we detect 24 photons per bin, corresponding toa significant Poissonian noise on the x-axis value in Fig.2.One can gain more information by implementing a dou-ble heralding technique. Efficient coherent scattering fromthe QD will result in light rotating from | V (cid:105) → | H (cid:105) , caus-ing a significant intensity reduction in the directly reflectedchannel (APD-1), i.e. the co-polarized counts should de-crease. This should also occur just as the cross-polarizedcounts increase (APD-2). This anti-correlation gives a moreaccurate measure of when the QD is on-resonance, as it re-duces the influence of uncorrelated background counts be-tween the two channels. Note that it is not sufficient to useonly APD-1 and APD-2 to infer the phase shift as evenfor small phase shifts there is a small statistical probabil-ity that APD-2 counts more photons than APD-1 thus wecould trivially postselect a small number of π phase shiftinstances. In contrast the double heralding technique heredoes not work as a post selection: APD-1 and APD-2 her-ald only that the QD is on resonance with the laser, and actsas the trigger at which point we collect all the photons inAPD-3 and APD-4 (uncorrelated with APDs- 1 and 2) tomeasure the phase.To explore this Fig. 3 shows a 2D histogram revealingthe correlation between the lower bound value of the phaseshift ( cos ( φ LB ) = AP D − AP D AP D AP D ) and the count-rates in theco- and cross-channels of the herald arm (APD-1,2), again,for µs time bins. A clear pattern emerges. For timebins where the co-polarised (APD-1) counts are high, andthe cross-polarised counts (APD-2) are low (approx APD-1 > < φ LB < . π . This corresponds to the off-resonancebehavior. However when the cross-polarised counts arehigh and the co-polarised counts are low one observes adrastic shift, represented by a large “hot-spot” in the data(approximately, APD-2 > < φ LB is consistently above . π . Thisscattering occurs when the QD and laser are close to reso-nance. Note that it might first appear surprising that datafrom APDs-3,4 give a > π/ phase shift for coordinateswhere APD-1 > APD-2 (one would expect a polarisation re-versal). However, this occurs due to experimental limita-tions. APDs- 3,4 have much lower background counts thanAPDs-1,2. This reduced background leads to a more ac-curate measure of the phase shift (see Supplementary fordetails).Further, there are clearly “pockets” in the data where thephase shift is much higher than . π . In particular oneobserves the highest phase shifts for very low VH ratios inthe herald arm. This implies that there are specific timewindows that allow the highest phase shifts to be measured.We calculate that to measure a > . π phase shift, thelaser should be within ± neV of the peak of the . µ eV FIG. 3: A plot of the number of the lower bound phase shift forspecific count-rates in detectors APD-1 and APD-2 in 100 µ s timebins. The colour map now represents the QD induced phase shiftmeasured via detectors APD-3, and APD-4. linewidth transition. We calculate that this should occur ∼ . of the time (assuming inhomogeneous broaden-ing of a 0.7 µ eV QD line to 5 µ ev). We also require thatenough photon counts can be gathered in the time windowin question to overcome Poissonian statistics, and that the T spin lifetime of the transition is longer than the time binused. By varying the time bin width we determine a spin T time of 250 µ s and a spectral jitter time of . ms (seeSupplementary).Finding the instances where near exact resonance con-ditions are fulfilled will allow the highest phase shift pos-sible to be measured. We can reliably measure the phaseshift inside the “hot-spot” of φ LB = 0 . π ± . π ( . ◦ ± . ◦ ). The highest phase shift measured in the100 µ s bins in Fig. 3 corresponds to φ LB = 0 . π ± . π ( ◦ ± ◦ ). The limit in the phase shift measured isdue to ellipticity induced on the reflected signal, which oc-curs when β < , along with residual background photons.In order to correct for this one needs to measure in boththe linear and circular polarised basis, however practicallymode-matching limitations prevent an accurate phase mea-surement in this case (see Supplementary). On a practicallevel the fact that these large phase shifts can be observedindicates that spectral jitter can easily be overcome simplyby collecting sufficient photons over a timescale where theQD is stable. By increasing the collection efficiency of thescattered photons (currently < ) then it will be possibleto actively trigger when the QD is on resonance as opposedto after the data has been collected as we do here.We conclude that using a low Q-factor, high efficiencyQD microcavity system, one may achieve deterministicphoton-spin interactions, by inducing a > π/ phase shifton a narrow bandwidth single photon. Not only do we mea-sure, to our knowledge, by far the largest ever photon phaseshift from a solid state quantum emitter, we reach the cru-cial measured threshold of φ > π/ [26]. When on reso-nance we infer that of the reflected photons in the col-lection channel undergo a deterministic π phase shift. Fur-ther we have shown that the spectral jitter in these systemscan be slow ( times slower than the exciton lifetime)and that we can trigger on time windows where the QD lineis stable. This would enable the generation of continuousstreams of hundreds of photons, a necessary requirementfor photonic cluster states[22]. The significant challengeremaining is efficient mode matching of the reflected pho-tons. High fidelity gate operations will require exceptionalreduction in background scatter implying > opticalmode-matching is required. By integrating these micropil-lars, perhaps directly with optical fibre, one could poten-tially reflect and collect photons per µ s. This wouldallow one to produce a 20 photon cluster state several timesper second, representing a leap forward for the number ofphotonic qubits available for quantum information applica-tions. Methods