Quantum Non-demolition Detection of Single Microwave Photons in a Circuit

Transcription

1 Quntum Non-demolition Detection of Single Microwve Photons in Circuit B. R. Johnson, 1 M. D. Reed, 1 A. A. Houck, 2 D. I. Schuster, 1 Lev S. Bishop, 1 E. Ginossr, 1 J. M. Gmett, 3 L. DiCrlo, 1 L. Frunzio, 1 S. M. Girvin, 1 nd R. J. Schoelkopf 1 1 Deprtments of Physics nd Applied Physics, Yle University, New Hven, CT 6511, USA 2 Deprtment of Electricl Engineering, Princeton University, Princeton, NJ 8544, USA 3 Institute for Quntum Computing nd Deprtment of Physics nd Astronomy, University of Wterloo, Wterloo, ON, Cnd, N2L 3G1 (Dted: Mrch 12, 21 Ech photon numer n corresponds to different phse φ, so repeted Rmsey experiments 5 cn e used to estimte the phse nd extrct n. This method is QND, ecuse it does not exchnge energy etween the tom nd photon. However, since the phse cnnot e mesured in single opertion, it does not extrct full informtion out prticulr Fock stte n in single interrogtion. Nonetheless, using Ryderg toms in QED, remrkle experiments hve shown quntum jumps of light nd the collpse of the photon numer y mesurement. 5,12 Here we report new method which implements set of progrmmle controlled-not (CNOT opertions etween n n-photon Fock stte nd quit, sking the question re there exctly n photons in the? A single interrogtion consists of pplying one such CNOT opertion nd reding-out the resulting quit stte. To do this we use qusi-dispersive quit-photon interction which cuses the quit trnsition frequency to depend strongly on the numer of photons in the. Consequently, frequency control of pulse implements conditionl π rottion on the quit the quit stte is inverted if nd only if there re n photons in the storge. To ensure tht this is QND, the quit nd storge re diticlly decoupled efore performing mesurement of the quit stte. To relize this method we extend circuit-sed QED 13 y coupling single trnsmon quit 14,15 simultneously to two cvities. This llows one to e optimized for fst redout nd the other for coherent storge of photons. Relted work y Leek et l. 16 relized single trnsmon coupled to two modes of single, where the the two modes were engineered to hve very different qulity fctors. A schemtic of the two- device is shown in Fig. 1(. A high-q serves s photon memory for preprtion nd storge, nd low-q is used for fst redout of the quit. The cvities re relized s N coplnr wveguide resontors with λ/2 resonnces t ω s /2π = 5.7 GHz nd ω m /2π = 6.65 GHz, respectively. The cvities re engineered, y design of the cpcitors C s nd C m, to hve very different decy rtes (κ s /2π = 5 khz nd κ m /2π = 2 MHz so tht the quit stte cn e mesured severl times per photon lifetime in the storge. A trnsmon quit is end-coupled to the two cvirxiv: v1 [cond-mt.mes-hll] 13 Mr 21 Thorough control of quntum mesurement is key to the development of quntum informtion technologies. Mny mesurements re destructive, removing more informtion from the system thn they otin. Quntum non-demolition (QND mesurements llow repeted mesurements tht give the sme eigenvlue 1. They could e used for severl quntum informtion processing tsks such s error correction 2, preprtion y mesurement 3, nd one-wy quntum computing 4. Achieving QND mesurements of photons is especilly chllenging ecuse the detector must e completely trnsprent to the photons while still cquiring informtion out them 5,6. Recent progress in mnipulting microwve photons in superconducting circuits 7 9 hs incresed demnd for QND detector which opertes in the gighertz frequency rnge. Here we demonstrte QND detection scheme which mesures the numer of photons inside high qulity-fctor microwve on chip. This scheme mps photon numer onto quit stte in singleshot vi quit-photon logic gtes. We verify the opertion of the device y nlyzing the verge correltions of repeted mesurements, nd show tht it is 9% QND. It differs from previously reported detectors 5,8 11 ecuse its sensitivity is strongly selective to chosen photon numer sttes. This scheme could e used to monitor the stte of photon-sed memory in quntum computer. Severl tems hve engineered detectors which re sensitive to single microwve photons y strongly coupling toms (or rtificil toms to high-q cvities. This rchitecture, known s quntum electrodynmics ( QED, cn e used in vrious wys to detect photons. One destructive method mesures quntum Ri oscilltions of n tom or quit resonntly coupled to the 8 1. The oscilltion frequency is proportionl to n, where n is the numer of photons in the, so this method essentilly mesures the time-domin swp frequency. Another method uses dispersive interction to mp the photon numer in the onto the phse difference of superposition of tomic sttes ( g +e iφ e / 2.

2 2 mes storge mm trnsmon nd flux is Frequency (GHz Flux is current (µa 1 µm FIG. 1. Circuit schemtic nd device., Circuit schemtic showing two cvities coupled to single trnsmon quit. The mesurement is proed in reflection y sending microwve signls through the wekly coupled port of directionl coupler. A flux is line llows for tuning of the quit frequency on nnosecond timescles., Implementtion on chip, with ω m/2π = 6.65 GHz mesurement on the left nd its lrge coupling cpcitor (red, nd ω s/2π = 5.7 GHz storge on the right with much smller coupling cpcitor (lue. A trnsmon quit (green is strongly coupled to ech, with g s/2π = 7 MHz nd g m/2π = 83 MHz. It hs chrging energy E C/2π = 29 MHz nd mximl Josephson energy E J/2π 23 GHz. At lrge detunings from oth cvities, the quit coherence times re T 1 T 2.7 µs. ties, with finger cpcitors controlling the individul coupling strengths (g s /2π = 7 MHz nd g m /2π = 83 MHz. The usul shunt cpcitor etween the trnsmon islnds is replced with cpcitors to the ground plnes to reduce direct coupling etween the cvities. Additionlly, flux is line 17 llows fst control of the detunings s = ω g,e ω s nd m = ω g,e ω m etween the trnsmon nd cvities, where we use the convention of leling the trnsmon sttes from lowest to highest energy s (g, e, f, h,... To chieve high photon numer selectivity of the CNOT opertions, there must e lrge seprtion etween the numer-dependent quit trnsition frequencies. To otin this, we use smll detunings ( s /g s < 1 etween the quit nd storge. Figure 2 shows spectroscopy in this qusi-dispersive regime s function of flux is when the storge is populted with coherent stte ( ˆn 1. Results of numericl energy-level clcultion re overlid, showing the positions of vrious trnsitions. We define ωg,e n s the photon FIG. 2. Pulsed spectroscopy with coherent stte in storge ( n 1 vs. quit- detuning s = ω g,e ω s. Clculted trnsition frequencies re overlid in color. Red nd ornge lines re the g e trnsitions of the quit when n = nd 1, respectively. Trnsitions to higher trnsmon levels ( f nd h re visile ecuse of the smll detuning. The rrow indictes the flux is current used during the CNOT opertions. numer-dependent trnsition frequency n, g n, e. Other trnsitions, such s 2, g, h, re llowed due to the smll detuning. Fortuntely, we lso see tht the seprtion etween ωg,e nd ωg,e 1 grows rpidly to order 2g = 14 MHz s the quit pproches the storge. To test the photon meter, we generte single photons in the storge with n ditic protocol. Our method uses the voided crossing etween the, e nd 1, g levels to convert quit excittion into photon. The preprtion of photon egins with the quit detuned elow the storge ( s 3g s, where we pply π-pulse to crete the stte, e. We then diticlly tune the quit frequency through the voided crossing with the storge, leving the system in the stte 1, g. The sweep rte is limited y Lndu-Zener trnsitions which keep the system in, e. Our preprtion protocol chnges the quit frequency y 6 MHz in 5 ns, giving trnsition proility less thn.1% (clculted with multi-level numericl simultion. This protocol ctully llows for the cretion of ritrry superpositions of, g nd 1, g y chnging the rottion ngle of the initil pulse. For exmple, if we use π/2-pulse, fter the sweep we end up in the stte (, g +e iφ 1, g / 2, where φ is determined y the rottion xis of the π/2-pulse. One could lso use resonnt swp scheme, which hs een successfully used to crete Fock sttes 9 up to n = 15. The method used here hs the dvntge of eing very roust to timing errors. After the photon is prepred, the quit frequency is djusted such tht s /g s 5. At this detuning, the seprtion etween ωg,e nd ωg,e 1 is 65 MHz. In Fig. 3(,

3 3 Phse shift (degrees P e prepre 5.4 R (θ R 1 (θ 5.45 Frequency (GHz 3π/2 π/2 5.5 R (θ R 1 (θ -2π -π π 2π -2π -π π 2π Interrogtion Ri ngle (rdins c 2π π prepre 5.55 FIG. 3. Single photon preprtion nd CNOT selectivity., Pulsed spectroscopy vs. Ri ngle of preprtion pulse, showing the reflected phse of pulse t the mesurement frequency fter 8 ns pulse ner the quit frequency. Trces re offset verticlly for clrity nd leled with the rottion ngle of the control pulse used in the preprtion step. The dips correspond to ωg,e 5.47 GHz nd ωg,e GHz, respectively. nd c, Ri driving the quit trnsitions fter prepring n = ( nd n = 1 (c. The red (lue trces show the mesured quit excited stte proility fter pplying n interrogtion Ri pulse with vrying ngle t ωg,e (ωg,e. 1 The residul oscilltion of R 1(θ in c is mostly due to preprtion infidelity. we show pulsed spectroscopy t this detuning for severl rottion ngles of the initil preprtion pulse. We oserve well-resolved dips in the reflected phse of pulsed signl sent t the mesurement frequency. The loctions of these dips correspond to the quit trnsition frequencies for n = (ωg,e nd n = 1 (ωg,e, 1 nd the reltive heights mtch expecttions from the different preprtion pulse rottions (e.g. π/2-pulse results in equl height signls. To show selective driving of these trnsitions, we perform Ri experiments t ω g,e nd ω 1 g,e for the cses where we prepre, g nd 1, g. In ech experiment we ensemle verge mesurements of the resulting quit stte fter further decoupling the quit from the storge. For the, g cse [Fig. 3(] there is lrge mplitude oscilltion when the drive is t ω g,e [red, R (θ] nd lmost no oscilltion when the drive is t ω 1 g,e [lue, R 1 (θ]. When we prepre 1, g the sitution is reversed [Fig. 3(c]; however, in this cse the residul oscilltion of R (θ (red is sustntil due to smll errors in the preprtion of 1, g ssocited with the initil rottion of the quit nd, more importntly, the 1% proility of energy decy during the susequent ditic sweep through the. The responses R i (θ re result of driving ωg,e i nd the fr off-resonnt drive of ωg,e, j where j i. The crosstlk is seen in the smll residul oscilltion of R 1 (θ in Fig. 3(. In the supplement, we derive method for extrcting selectivity nd preprtion fidelity from these dt, giving selectivity 95% for oth interrogtions nd preprtion fidelity of n = 1 ψ 2 88%. These numers were confirmed y doing equivlent experiments over rnge of preprtion pulse rottion ngles etween nd 2π (not shown. If π-pulses re used in the interrogtion step, mesurement results of the verge quit stte directly correlte with the proility of eing in the sttes n = or n = 1. Detils of the scling needed to do this trnsformtion when the selectivity is < 1% re presented in the supplement. These re the desired CNOT opertions of the photon meter. If we now insert vrile dely efore interrogting, we find tht P (, the proility of eing in n = ( n = 1 decys exponentilly towrds 1 (, s shown y the red (ornge trce in Fig. 4(. The decy constnt of T ±.2 µs grees with the linewidth of the storge, 1/κ s = 1/(2π 5 khz = 3.18 µs, mesured in seprte, low power ( n 1 reflection experiment. Strong QND mesurements re projective, such tht if the mesurement oservle commutes with the Hmiltonin, the system will remin in n eigenstte of oth opertors etween mesurements. Consequently, compring the results of successive interrogtions provides mechnism to test whether prticulr protocol cuses dditionl perturtions on the system. Here, we only compre ensemle verge results, ecuse the singleshot quit redout fidelity for the device is 55%. This is sufficient to revel processes which chnge the photon numer, nd slight technicl improvements to interrogtion speed or quit redout fidelity should llow for rel-time monitoring of the photon stte. The protocol cnnot e repeted immeditely, though, ecuse the first interrogtion my leve the quit in the excited stte. To circumvent this prolem, we use the fst decy rte of the mesurement to cuse the quit to spontneously decy into the 5 Ohm environment. The reset protocol rings the quit into resonnce with the mesurement for time, τ reset = 5 ns, which is sufficient to reset the quit with proility 98%. The procedure is descried in detil in Ref. 18. After resetting the quit, we cn interrogte second time. The full protocol for repeted interrogtion sequence is shown in Fig. 4(. The comintion of CNOT (CNOT 1, quit mesurement, nd quit reset define n interrogtion process I (I 1. Dt for

4 4 Detuning ( s /g s Proility c 4.85 GHz ~5.45 GHz 6.65 GHz ~5.45 GHz 6.65 GHz CNOT,1 CNOT Mes,1 Mes Wve reset 22 mes Preprtion Flux prepre prepre 1st Interrogtion Reset dely nd Interrogtion storge Time (ns Single: P Repeted: P I I P I 1 I Dely (µs interrogte zero (I interrogte one (I 1 the four possile comintions of interrogting n = nd n = 1 re shown in Fig. 4( s function of dely etween the first nd second interrogtions. The dt re ensemle verged over ll results from the first interrogtion, so we do not oserve projection onto numer sttes. Insted, we gin oserve exponentil decy, where the result of the second mesurement is essentilly indistinguishle from the first, indicting tht the interrogtion is highly QND. Devitions from the verge mesurements of single interrogtion stem from finite photon lifetime in the storge nd non-qnd processes which cuse trnsitions to other photon numers [Fig. 4(c]. Recording the second interrogtion results for different delys llows us to sutrct the effect of photon T 1 nd clculte the trnsition proilities for the I nd I 1 processes 19. In principle, I nd I 1 cn cuse trnsitions to photon numers outside of the n {, 1} mnifold; however, the sence of sttisticlly significnt devitions from P + = 1 suggests tht ny such effects re negligile. Insted, we oserve γ (γ 1 = 1 (1 ± 3% nd δ (δ 1 = 7 (3 ± 3%, demonstrting tht this protocol is highly QND. The protocol presented here is fst nd highly QND mesurement of single photons, which we elieve cn e extended to detect higher photon numers. It should e possile to demonstrte the projective nture of the interrogtion nd crete highly non-clssicl sttes of light vi post selection, nd eventully with higher fidelity redout it should e possile to oserve quntum jumps of light in circuit. We thnk Jerry Chow nd Michel Devoret for helpful discussions. This work ws supported y NSF grnts DMR nd PHY J.M.G. ws supported y CIFAR Junior Fellowship, MITACS, MRI nd NSERC. L.F. ws prtilly supported y CNR-Istituto di Ciernetic. SUPPLEMENT Mesured Voltge Scling FIG. 4. Repeted mesurements of photons., Experiment protocol. A microwve pulse nd ditic sweep lod single photon into the storge in the preprtion step. This photon is interrogted repetedly y numer-selective CNOT gtes on the quit, followed y ditic decoupling, quit redout, nd reset., Single nd repeted interrogtion fter prepring n = 1 (top or n = (ottom, ensemle verged over 5, itertions. The ner-perfect overlp etween single nd repeted results demonstrte tht the protocol is highly QND. c, Trnsition proility digrms for the interrogte n = (I nd interrogte n = 1 (I 1 processes. We extrct γ (γ 1 = 1 (1 ± 3% nd δ (δ 1 = 7 (3 ± 3%. When the interrogtion selectivity is less thn 1%, we need to ccount for undesired rottions to correctly clculte the stte proilities from the mesured voltges. The detils of our clirtion procedure follow. If we prepre n = or n = 1 t time t =, when we interrogte t some lter time there is n dditionl proility p d to decy, giving the density mtrices ρ = g g, ρ 1 = g g {p d + (1 p d 1 1 }, where ρ i indictes prepring stte i t t =. We cn model the interrogtion pulses s opertions which ct on ρ i : U = R y (π + R y (ɛ 1 1, U 1 = R y (ɛ + R y (π 1 1, U I = 11, where ɛ nd ɛ re smll ngles. After interrogtion, the integrted homodyne response is W n r = V g + V Tr(Π e U r ρ P U r,

5 5 where n {, 1} is the Fock stte of the, r {, 1, I}, V g (V e is the voltge mesured when the quit is in g ( e, V = V e V g, nd Π e = e e. By using the nottion slightly nd treting ɛ, ɛ s proilities rther thn rottion ngles, we cn clculte the W n r W I = V g, W = V g + V, W 1 = V g + V ɛ, W 1 = V g + V (ɛ (1 p d + p d, W 1 1 = V g + V ((1 p d + ɛp d. We mesure these five voltges in clirtion experiments nd invert the equtions to find the prmeters V g, V, p d, ɛ, nd ɛ. Note tht this does not require perfect preprtion fidelity ecuse the model includes decy etween preprtion nd interrogtion p d which will lso cpture ny fixed preprtion infidelity. This gives the selectivities, (1 ɛ nd (1 ɛ, s well s the preprtion fidelity, (1 p d. An unknown mixture of n = nd n = 1 is chrcterized y single proility p, ρ = g g {p + (1 p 1 1 }, which produces the responses W ρ = V g + V (p + ɛ (1 p, W ρ 1 = V g + V (ɛ p + (1 p. This leds to simple rescling to trnsform W ρ nd W ρ 1 into P nd P = W ρ (V g + V ɛ V (1 ɛ, = W ρ 1 (V g + V ɛ. V (1 ɛ Error Estimte The primry chllenge in these experiments is otining sufficiently ccurte nd precise control of the quit frequency to do high-fidelity opertions. The nrrow ndwidth pulses used in the CNOT opertions mens tht even few MHz error in frequency control results in significnt rottion error. We use deconvolution techniques similr to those descried in the supplement of Ref. 9; however, the flux is current response function drifts on time scle of out one dy, mking it difficult to eliminte ll clssicl control errors. Even fter pplying corrections, there is remining spred of 2 3 MHz in the quit frequencies over the vrious reliztions of preprtion to interrogtion dely. This trnsltes into 2 3% error in the proility to find the quit in e fter pplying conditionl π-pulse. The errors rs reported in the lower pnel of Fig. 4( re due to this systemtic error. 1. Brginsky, V. B. & Khlili, F. Y. Quntum nondemolition mesurements: the route from toys to tools. Rev. Mod. Phys. 68, 1 11 ( Stene, A. M. Simple quntum error-correcting codes. Phys. Rev. A 54, ( Ruskov, R. & Korotkov, A. N. Entnglement of solidstte quits y mesurement. Phys. Rev. B 67, ( Russendorf, R. & Briegel, H. J. A one-wy quntum computer. Phys. Rev. Lett. 86, ( Guerlin, C. et l. Progressive field-stte collpse nd quntum non-demolition photon counting. Nture 448, ( Gmett, J. et l. Quit-photon interctions in : Mesurement induced dephsing nd numer splitting. Phys. Rev. A 74, ( Houck, A. A. et l. Generting single microwve photons in circuit. Nture 449, ( Hofheinz, M. et l. Genertion of Fock sttes in superconducting quntum circuit. Nture 454, ( Hofheinz, M. et l. Synthesizing ritrry quntum sttes in superconducting resontor. Nture 459, ( Brune, M. et l. Quntum Ri oscilltion: A direct test of field quntiztion in. Phys. Rev. Lett. 76, ( Schuster, D. I. et l. Resolving photon numer sttes in superconducting circuit. Nture 445, ( Gleyzes, S. et l. Quntum jumps of light recording the irth nd deth of photon in. Nture 446, ( Schoelkopf, R. J. & Girvin, S. M. Wiring up quntum systems. Nture 451, ( Koch, J. et l. Chrge-insensitive quit design derived from the Cooper pir ox. Phys. Rev. A 76, ( Schreier, J. A. et l. Suppressing chrge noise decoherence in superconducting chrge quits. Phys. Rev. B 77, 1852 ( Leek, P. J. et l. Cvity quntum electrodynmics with seprte photon storge nd quit redout modes. Phys. Rev. Lett. 14, 154 ( DiCrlo, L. et l. Demonstrtion of two-quit lgorithms with superconducting quntum processor. Nture 46, ( Reed, M. D. et l. Fst quit reset nd suppressing spontneous emission of superconducting quit (21. rxiv: Lupsçu, A. et l. Quntum non-demolition mesurement of superconducting two-level system. Nture Physics 3, (27.