Controlling the Spontaneous Emission of a Superconducting Transmon Qubit

Houck, Andrew; Schreier, J. A.; Johnson, Blake; Chow, Jerry M.; Koch, Jens; Gambetta, Jay; Schuster, David I.; Frunzio, Luigi; Devoret, Michel; Girvin, S. M.; Schoelkopf, Robert

doi:10.1103/physrevlett.101.080502

Cited by 416 publications

(494 citation statements)

References 31 publications

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“…The 38 MHz linewidth of this resonance translates to very short coherence times (T 1 ∼ 40 ns) compared to typical implementations [37]. Purcell losses contribute less than 2 MHz to this linewidth.…”

Section: Resultsmentioning

confidence: 99%

Approaching ultrastrong coupling in transmon circuit QED using a high-impedance resonator

et al. 2017

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In this experiment, we couple a superconducting transmon qubit to a high-impedance 645 microwave resonator. Doing so leads to a large qubit-resonator coupling rate g, measured through a large vacuum Rabi splitting of 2g 910 MHz. The coupling is a significant fraction of the qubit and resonator oscillation frequencies ω, placing our system close to the ultrastrong coupling regime (ḡ = g/ω = 0.071 on resonance). Combining this setup with a vacuum-gap transmon architecture shows the potential of reaching deep into the ultrastrong couplingḡ ∼ 0.45 with transmon qubits.

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Section: Resultsmentioning

confidence: 99%

Approaching ultrastrong coupling in transmon circuit QED using a high-impedance resonator

et al. 2017

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“…The vacuum Rabi coupling strengths for the two qubits are obtained as g 0 /π = 347 MHz (qubit 1) and g 0 /π = 94.4 MHz (qubit 2). Time-domain measurements of the qubits show that they are Purcell-limited and completely homogeneously broadened at their flux sweet spots 24 . The coherence times are T 1 = 1.7 µs and T 2 = 0.7 µs (qubit 1, away from the flux sweet spot) and T 1 = 1.4 µs and T 2 = 2.8 µs (qubit 2, at flux sweet spot).…”

Section: Methodsmentioning

confidence: 99%

Nonlinear response of the vacuum Rabi resonance

et al. 2008

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On the level of single atoms and photons, the coupling between atoms and the electromagnetic field is typically very weak. By using a cavity to confine the field, the strength of this interaction can be increased by many orders of magnitude, to a point where it dominates over any dissipative process. This strong-coupling regime of cavity quantum electrodynamics 1,2 has been reached for real atoms in optical cavities 3 , and for artificial atoms in circuit quantum electrodynamics 4 and quantum dot systems 5,6 . A signature of strong coupling is the splitting of the cavity transmission peak into a pair of resolvable peaks when a single resonant atom is placed inside the cavity, an effect known as vacuum Rabi splitting. The circuit quantum electrodynamics architecture is ideally suited for going beyond this linear-response effect. Here, we show that increasing the drive power results in two unique nonlinear features in the transmitted heterodyne signal: the supersplitting of each vacuum Rabi peak into a doublet and the appearance of extra peaks with the characteristic √ n spacing of the Jaynes-Cummings ladder. These findings constitute direct evidence for the coupling between the quantized microwave field and the anharmonic spectrum of a superconducting qubit acting as an artificial atom.Circuit quantum electrodynamics (QED) realizes the coupling between a superconducting qubit and the microwave field inside an on-chip transmission-line resonator 4,7 . The drastic reduction in mode volume for such a quasi-one-dimensional system 8,9 , the recent improvement in coherence times 10 and the absence of atomic motion render circuit QED an ideal system for studying the strong-coupling limit. In the customary linear-response measurement of the transmitted microwave radiation, the vacuum Rabi splitting manifests itself as an avoided crossing between the qubit and the resonator.It may be argued that the observation of the splitting is not yet a clear sign for quantum behaviour 11,12 , because avoided crossings are also ubiquitous in classical physics. However, quantum mechanics gives rise to a distinct anharmonicity of these splittings when initializing the resonator in a higher photon Fock state: when the resonator mode is occupied by n photons, the splitting is enhanced by a factor √ n + 1 as compared with the vacuum Rabi situation. This anharmonicity has been observed with single atoms in both microwave 13 and optical cavities 14,15 . In circuit QED, this characteristic trait has been observed in time-domain measurements 16 . In a system similar to ours, the position of the n = 2 peaks was recently demonstrated in a two-tone pump-probe measurement 17 .Here, we present a theoretical analysis and experimental investigation of the vacuum Rabi resonance in a circuit QED system, where we study the √ n anharmonicity up to n = 5 by exploring the power dependence of the heterodyne transmission (see the Methods section). This type of detection is particularly simple, because it is a continuous measurement involving only a single dr...

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“…Black-box quantization analysis of the qubit-cavity system suggest that the relaxation times were limited by the Purcell effect 33 . Coherence times did not improve using an echo pulse suggesting that they were limited by thermal photons present in the fundamental and higher modes of the cavity 34 as well as non-zero qubit temperature (∼ 75 mK).…”

Section: Methods Summarymentioning

confidence: 99%

“…The T 1 of the qubits are believed to be Purcell-limited 33 (implying κT 1 = constant) and potentially could be a factor of 10 longer in the 3D cQED architecture 24 . However, this improvement cannot be achieved by reducing κ, as that would concurrently reduce the feedback correction time, and thus the steady-state fidelity.…”

Section: Sources Of Steady-state Infidelitymentioning

confidence: 99%

Autonomously stabilized entanglement between two superconducting quantum bits

Shankar¹,

Hatridge²,

Leghtas³

et al. 2013

Nature

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Quantum error-correction codes would protect an arbitrary state of a multi-qubit register against decoherence-induced errors 1 , but their implementation is an outstanding challenge for the development of large-scale quantum computers. A first step is to stabilize a nonequilibrium state of a simple quantum system such as a qubit or a cavity mode in the presence of decoherence. Several groups have recently accomplished this goal using measurementbased feedback schemes [2][3][4][5] . A next step is to prepare and stabilize a state of a composite system [6][7][8] . Here we demonstrate the stabilization of an entangled Bell state of a quantum register of two superconducting qubits for an arbitrary time. Our result is achieved by an autonomous feedback scheme which combines continuous drives along with a specifically engineered coupling between the two-qubit register and a dissipative reservoir. Similar autonomous feedback techniques have recently been used for qubit reset 9 and the stabilization of a single qubit state 10 , as well as for creating 11 and stabilizing 6 states of multipartite quantum systems. Unlike conventional, measurement-based schemes, an autonomous approach counter-intuitively uses engineered dissipation to fight decoherence [12][13][14][15] , obviating the need 1 arXiv:1307.4349v3 [quant-ph] 23 Oct 2013 for a complicated external feedback loop to correct errors, simplifying implementation. Instead the feedback loop is built into the Hamiltonian such that the steady state of the system in the presence of drives and dissipation is a Bell state, an essential building-block state for quantum information processing. Such autonomous schemes, broadly applicable to a variety of physical systems as demonstrated by a concurrent publication with trapped ion qubits 16 , will be an essential tool for the implementation of quantum-error correction.Here we implement a proposal 17 , tailored to the circuit Quantum Electrodynamics (cQED) architecture 18 , for stabilizing entanglement between two superconducting transmon qubits 19 . The qubits are dispersively coupled to an open cavity which acts as the dissipative reservoir. The cavity in our implementation is furthermore engineered to preferentially decay into a 50 Ω transmission line that we can monitor on demand. We show, using two-qubit quantum state tomography and high-fidelity single-shot readout, that the steady-state of the system reaches the target Bell state with a fidelity of 67 %, well above the 50 % threshold that witnesses entanglement. As discussed in Ref. 17, the fidelity can be further improved by monitoring the cavity output and performing conditional tomography when the output indicates that the two qubits are in the Bell state. We implemented this protocol via post-selection and demonstrated that the fidelity increased to ∼ 77 %.Our cQED setup, outlined schematically in Fig. 1a, consists of two individually addressable qubits, Alice and Bob, coupled dispersively to a three-dimensional (3D) rectangular copper cavity.The setup is described by...

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Controlling the Spontaneous Emission of a Superconducting Transmon Qubit

Cited by 416 publications

References 31 publications

Approaching ultrastrong coupling in transmon circuit QED using a high-impedance resonator

Approaching ultrastrong coupling in transmon circuit QED using a high-impedance resonator

Nonlinear response of the vacuum Rabi resonance

Autonomously stabilized entanglement between two superconducting quantum bits

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