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Parity Detection of Propagating Microwave Fields

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Parity Detection of Propagating Microwave Fields Parity Detection of Propagating Microwave Fields Jean-Claude Besse,1, ∗ Simone Gasparinetti,1, y Michele C. Collodo,1 Theo Walter,1 Ants Remm,1 Jonas Krause,1 Christopher Eichler,1 and Andreas Wallraff1 1Department of Physics, ETH Zurich, CH-8093 Zurich, Switzerland (Dated: December 23, 2019) The parity of the number of elementary excitations present in a quantum system provides impor- tant insights into its physical properties. Parity measurements are used, for example, to tomographi- cally reconstruct quantum states or to determine if a decay of an excitation has occurred, information which can be used for quantum error correction in computation or communication protocols. Here we demonstrate a versatile parity detector for propagating microwaves, which distinguishes between radiation fields containing an even or odd number n of photons, both in a single-shot measurement and without perturbing the parity of the detected field. We showcase applications of the detector for direct Wigner tomography of propagating microwaves and heralded generation of Schr¨odinger cat states. This parity detection scheme is applicable over a broad frequency range and may prove useful, for example, for heralded or fault-tolerant quantum communication protocols. I. INTRODUCTION qubits for measurement based entanglement generation [13], for elements of error correction [14{16], and entan- In quantum physics, the parity P of a wavefunction glement stabilization [17], an experiment which was also governs whether a system has an even or odd number of performed with ions [18, 19]. excitations n. The parity affects, for example, the sys- tem's statistical properties such as the likelihood of tran- sitions occurring between distinct quantum states [1,2]. II. PARITY DETECTION SCHEME An ideal measurement of the parity P of a system distin- guishes states with even (0; 2; 4; :::) from states with odd The parity detector for propagating microwave fields n (1; 3; 5; :::), while not providing any other information introduced here is based on a cavity QED system realized about the precise value of n. in superconducting circuits. We characterize the detec- In superconducting circuits, for example, the parity tor performance by measuring the parity of single and of the number of photons stored in a microwave cavity multi-photon states distributed sequentially over multi- is determined either by direct measurements [3], pro- ple time bins as generated by a true single microwave viding immediate access to the value of P , or indirect photon source. We illustrate the use of the detector to di- measurements [4], requiring the reconstruction of P from rectly evaluate the Wigner function of propagating fields another measured quantity. Direct measurements of the of single photons and their coherent superpositions with parity are frequently used to reconstruct quantum states vacuum by measuring their displaced parity. Finally, we of radiation fields stored in microwave cavities [3,5,6]. highlight the single-shot and QND nature of the parity However, parity measurements of propagating quantum detector by heralding propagating, microwave-frequency radiations fields, which can be used as the carriers of in- Schr¨odingercat states, with a definite even or odd parity, formation in quantum networks, have just recently been from incident coherent states with varying amplitude j j. realized in the optical domain [7] with neutral atom based α systems [8], while experimental realizations in the mi- To measure the parity P of a propagating microwave crowave domain are still lacking. Multi-photon quan- field, we engineer a controlled phase gate between a su- tum non-demolition (QND) measurements of itinerant perconducting transmon qubit embedded in a cavity, act- microwave fields are an essential element for error de- ing as an ancilla, and itinerant microwave photons [20{22] acting as the control field. We realize this gate by tuning arXiv:1912.09896v1 [quant-ph] 20 Dec 2019 tection [9] and error correction in information processing networks as they provide a path towards detecting pho- the first, jei, to second excited-state, jfi, transition of ton loss. the transmon qubit, !ef =(2π) = 5:9 GHz, into resonance Parity measurements also play an important role in with the fundamental mode of a cavity. The ground, protocols for error correction in quantum information jgi, to first excited state transition !ge is detuned by the processing [10, 11] and quantum communication appli- anharmonicity α=(2π) = (!ef − !ge) =(2π) = −220 MHz, cations [12]. In that context parity measurements have from the cavity mode. Thus, a vacuum Rabi mode split- been demonstrated, for example, with superconducting ting, of size 2g1=(2π) = 76 MHz, occurs if and only if the transmon is prepared in the excited state jei [21]. This ancilla-based scheme allows for the quantum-non- demolition measurement of the photon-number parity of ∗ [email protected] the propagating field reflected off the input of the detec- y Current address: Quantum Technology Laboratory, Chalmers tor, a feature which we demonstrate explicitly here. University of Technology, SE-412 96 Gteborg, Sweden We arm the parity detector for a time Tw = 1 µs, 2 shorter than both the lifetime T1 = 4:5 µs and dephasing (a) π/2 π/2 ? Detector time T2 = 3:5 µs of the detector transmon qubit, by n = 1 ... N defining a Ramsey sequence formed by two π=2 pulses Source separated by T , Fig.1(a). Each photon impinging on w Displacer the detector input during the time Tw imparts a phase p Tw = 1 μs shift of φ = π on the superposition state (jgi+eiφjei)= 2 Readout t of the transmon qubit created by the first 2 pulse [21]. π= (b) As iφ is 2 -periodic, the Ramsey sequence encodes the Detector Readout e π Source ~ ~ parity of the total number of scattered photons in the qubit population after the second π=2 pulse, leaving the ~ transmon in jei for even hP i = +1 or in jgi for odd Displacer hP i = −1. A schematic of the measurement setup is Heterodyne Q shown and discussed in Fig.1(b), the sample and the wiring are presented in AppendixA. ~ LO2 Parity P = ±1 LO I ~ III. PARITY MEASUREMENTS (c) 1 We examine the performance of this parity detector 0.1 using a well characterized spontaneous-emission, single- › P ‹ photon source [23], operated on a separate chip. This , source is capable of creating phase coherent superposi- tions of vacuum, j0i, and single photon, j1i, states in a Parity single time bin with a pulse bandwidth κp=(2π) = 2 MHz, which is small compared to the effective parity detector - 0.1 bandwidth, set by the linewidth κeff =(2π) = 30 MHz of the detector cavity. In this way the phase imparted on - 1 the detector qubit by each photon is well defined. Since 0 1 2 3 4 5 6 the photon pulse length, 1/κp, is short compared to Tw, Number of photons, N it is fully detected by the Ramsey sequence during which the detector is armed. Figure 1. Experimental setup and parity measure- We operate the single photon source to emit sequences ments. (a) Parity detection pulse sequence: Ramsey pulses of N = 0; 1; :::; 6 pulses each containing a single photon applied to detector qubit (red), pulse train of N spontaneously Fock state j1i [23, 24] travelling towards the detector and emitted photons (blue), externally applied coherent mode- matched displacer field (orange), and readout pulse (purple). record the average parity hP i of the pulse train as indi- (b) Radiation coming from a source is reflected off of a cavity cated by our detector. We take the finite phase coherence (green) coupled to a transmon (red) acting as the detector. ? time T2 of the qubit and its readout fidelity into account The source is either a single photon emitter or a pulsed mi- to linearly map the measured qubit excited population crowave generator with amplitude and phase control. Disper- Pe to a parity value hP i using reference traces consisting sive readout of the transmon, assisted by an additional cavity of Ramsey sequences with the same Tw, AppendixB. (purple), yields the photon parity (purple box). Fields inside We observe the measured parity hP i (blue bars) chang- the detector cavity can be displaced in-situ by applying an ad- ing sign, as expected, for each added single photon pulse ditional coherent tone (orange). Standard heterodyne detec- establishing the detector's capability to discriminate even tion of the (I;Q)-quadratures of the reflected light field (green (hP i = +1) from odd (hP i = −1) photon number parity, box) is performed with a local oscillator (LO). (c) Measured parity hP i (blue bars, on positive and negative log scales) for a see Fig.1(c) with the ideal result indicated by dark gray train of N single photon pulses. Ideal value of hP i (dark gray wireframes. The contrast in the measured hP i, plotted wireframes) and hP i considering finite transmission efficiency on a logarithmic scale, reduces in good agreement with η = 78 % between source and detector (red wireframes and N (1−2η) (dashed red line) due to the finite transmission dashed lines). Error bars indicate the statistical standard efficiency η = 78 % between the source and the detector, deviation of ±4% of the parity. AppendixB. We note that these losses are external to the parity detector and independent of the detection event. y y by an operator Dα = exp(α a − αa ) directly yields the value of the Wigner function IV. WIGNER TOMOGRAPHY π W (α) = h jDy PD j i = Tr(PD ρDy ) (1) 2 α α α α Measuring the expectation value of the parity operator P of a radiation field described by a wave function j i, at the point α in phase space [4, 25, 26].
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