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To Catch and Reverse a Quantum Jump Mid-Flight Z LETTER https://doi.org/10.1038/s41586-019-1287-z To catch and reverse a quantum jump mid-flight Z. K. Minev1,5*, S. O. Mundhada1, S. Shankar1, P. Reinhold1, R. Gutiérrez-Jáuregui2, R. J. Schoelkopf1, M. Mirrahimi3,4, H. J. Carmichael2 & M. H. Devoret1* In quantum physics, measurements can fundamentally yield First, we developed a superconducting artificial atom with the discrete and random results. Emblematic of this feature is Bohr’s necessary V-shaped level structure (see Fig. 1a and Methods). It con- 1913 proposal of quantum jumps between two discrete energy sists, besides the ground level |G〉, of one protected, dark level |D〉— levels of an atom1. Experimentally, quantum jumps were first engineered to couple only minimally to any dissipative environment observed in an atomic ion driven by a weak deterministic force or any measurement apparatus—and one ancilla level |B〉, whose while under strong continuous energy measurement2–4. The times occupation is monitored at rate Γ. Quantum jumps between |G〉 and at which the discontinuous jump transitions occur are reputed to |D〉 are induced by a weak Rabi drive ΩDG—although this drive can be fundamentally unpredictable. Despite the non-deterministic eventually be turned off during the jump, as explained later. Because character of quantum physics, is it possible to know if a quantum a direct measurement of the dark level is not feasible nor desired, the jump is about to occur? Here we answer this question affirmatively: jumps are monitored using the Dehmelt shelving scheme2. Thus, the we experimentally demonstrate that the jump from the ground state occupation of |G〉 is linked to that of |B〉 by the strong Rabi drive ΩBG 2–4 to an excited state of a superconducting artificial three-level atom (ΩDG ≪ ΩBG ≪ Γ). In the atomic physics shelving scheme , an excita- can be tracked as it follows a predictable ‘flight’, by monitoring tion to |B〉 is recorded by detecting the emitted photons from |B〉 with a the population of an auxiliary energy level coupled to the ground photodetector. From the detection events—referred to in the following state. The experimental results demonstrate that the evolution of as ‘clicks’—one infers the occupation of |G〉. On the other hand, from each completed jump is continuous, coherent and deterministic. the prolonged absence of clicks (to be defined precisely below; see also We exploit these features, using real-time monitoring and Supplementary Information section II), one infers that a quantum jump feedback, to catch and reverse quantum jumps mid-flight—thus from |G〉 to |D〉 has occurred. Owing to the poor collection efficiency deterministically preventing their completion. Our findings, and the dead time of photon counters in atomic physics29, it is exceed- which agree with theoretical predictions essentially without ingly difficult to detect every individual click required to faithfully adjustable parameters, support the modern quantum trajectory register the origin in time of the advance warning signal. However, theory5–9 and should provide new ground for the exploration of real- superconducting systems present the advantage of high collection effi- time intervention techniques in the control of quantum systems, ciencies30–32, as their microwave photons are emitted into one-dimen- such as the early detection of error syndromes in quantum error sional waveguides and are detected with the same detection efficiencies correction. as optical photons. Furthermore, rather than monitoring the direct Bohr conceived of quantum jumps1 in 1913, and whereas Einstein fluorescence of the |B〉 state, we monitor its occupation by dispersively elevated the hypothesis to the level of a quantitative rule with his AB coupling it to an ancilla readout cavity. This further improves the fidel- coefficient theory10,11, Schrödinger strongly objected to their exist- ity of the detection of the de-excitation from |B〉 (effective collection ence12. The nature and existence of quantum jumps remained contro- efficiency of photons emitted from |B〉). versial for seven decades until they were directly observed in a single The readout cavity, schematically depicted in Fig. 1a by an LC circuit, 2–4 system . Since then, quantum jumps have been observed in various is resonant at ωC = 8,979.64 MHz and cooled to 15 mK. Its dispersive atomic13–16 and solid-state17–21 systems. Recently, they have been rec- coupling to the atom results in a conditional shift of its resonance fre- 22,23 ognized as an essential phenomenon in quantum feedback control , quency by χB/2π = −5.08 ± 0.2 MHz when the atom is in |B〉 and and in particular, for detecting and correcting decoherence-induced χD/2π = −0.33 ± 0.08 MHz when the atom is in |D〉 (see Fig. 1c). The 24,25 errors in quantum information systems . engineered large asymmetry between χB and χD together with the cav- Here, we focus on the canonical case of quantum jumps between ity coupling rate to the output waveguide, κ/2π = 3.62 ± 0.05 MHz, two levels indirectly monitored by a third—the case that corresponds renders the cavity response markedly resolving for |B〉 versus not-|B〉, to the original observation of quantum jumps in atomic physics2–4 (see yet non-resolving30 for |G〉 versus |D〉, thus preventing information the level diagram of Fig. 1a). A surprising prediction emerges accord- about the dark transition from reaching the environment. When prob- 5,26–28 ing to quantum trajectory theory : not only does the state of the ing the cavity response at ωC − χB, the cavity either remains empty, system evolve continuously during the jump between the ground |G〉 when the atom is in |G〉 or |D〉, or fills with n =±50.2 photons when and excited |D〉 state, but it is predicted that there is always a latency the atom is in |B〉. This readout scheme yields a transduction of the period prior to the jump, during which it is possible to acquire a signal |B〉-occupancy signal with fivefold amplification, which is an important that warns of the imminent occurrence of the jump (see Supplementary advantage to overcome the noise of the following amplification stages. Information section IIA). This advance warning signal consists of a To summarize, in this readout scheme, the cavity probe inquires: is the rare, particular lull in the excitation of the ancilla (bright) state |B〉. atom in |B〉 or not? The time needed to arrive at an answer with a con- − The acquisition of this signal requires the time-resolved, fully efficient fidence level of 68% (signal-to-noise ratio of 1) is Γκ1≈/1(n¯)8=.8ns detection of every de-excitation of |B〉. Exploiting the specific advan- for an ideal cavity-amplifier chain (Supplementary Information tages of superconducting artificial atoms and their quantum-limited section IIIC). readout chain, we designed an experiment that implements with maxi- Importantly, the engineered near-zero coupling between the cavity mum fidelity and minimum delay the detection of the advance warning and the |D〉 state protects the |D〉 state from harmful effects, including signal occurring before the quantum jump (see rest of Fig. 1). Purcell relaxation, photon shot-noise dephasing and the as-yet 1Department of Applied Physics, Yale University, New Haven, CT, USA. 2The Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Auckland, Auckland, New Zealand. 3Yale Quantum Institute, Yale University, New Haven, CT, USA. 4QUANTIC Team, INRIA de Paris, Paris, France. 5Present address: T. J. Watson Research Center IBM, Yorktown Heights, NY, USA. *e-mail: [email protected]; [email protected] NATURE| www.nature.com/nature RESEARCH LETTER D D a Bright B b 300 KFPGA controller energy relaxation T1 =±1165μs, Ramsey coherence T2R =±120 5sμ N D Γ and Hahn echo T2E =±1626μs. While protected, the |D〉 state is indi- Ω Logic and Real-time lter Dark D BG rectly read out in a quantum-non-demolition (QND) fashion by the actuator Demodulator combination of the V-structure, the drive between |G〉 and |B〉 and the Ω (t) DGDG T fast |B〉-state monitoring. In practice, we can access the population of 4 K M |D using an 80-ns unitary rotation followed by a projective measure- Ground G HE 〉 ... ment of |B〉 (see Methods). 15 mK JPC Once the state of the readout cavity is imprinted with information c ΩDG ΩBG FB FD about the occupation of |B〉, photons leak through the cavity output ... port into a superconducting waveguide, which is connected to the N amplification chain (see Fig. 1b), where they are amplified by a factor 12 Dark Bright Cavity response Z of 10 . The first stage of amplification is a quantum-limited Josephson parametric converter, which is followed by a high-electron-mobility d transistor amplifier at 4 K. The overall efficiency of the amplification –1 –1 –1 –1 D –1 chain is η = 0.33 ± 0.03, which includes all possible loss of information, Γ N Tint ΓBG Δtmid ΩDG T2R ΓDG Cavity such as due to photon loss, thermal photons or jitter (see Methods). At room temperature, the heterodyne signal is demodulated by a home- 100 101 102 103 104 105 106 t (ns) built field-programmable gate array (FPGA) controller, with a 4-ns Fig. 1 | Principle of the experiment. a, Three-level atom possessing a clock period for logic operations. The measurement record consists of hidden transition (shaded region) between its ground |G〉 and dark |D〉 a time series of two quadrature outcomes, Irec and Qrec, every 260 ns, state, driven by the Rabi drive ΩDG(t). Quantum jumps between |G〉 and |D〉 which is the integration time Tint, from which the FPGA controller esti- are indirectly monitored by a stronger Rabi drive ΩBG between |G〉 and the mates the state of the atom in real time.
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