Direct Wigner Tomography of a Superconducting Anharmonic Oscillator

Shalibo, Yoni; Resh, Roy; Fogel, Ofer; Shwa, David; Bialczak, Radoslaw C.; Martinis, John M.; Katz, Nadav

doi:10.1103/physrevlett.110.100404

Cited by 48 publications

(61 citation statements)

References 20 publications

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“…These circuit elements realize an anharmonic oscillator system, i.e., a system in which transitions are allowed only between neighboring states and the transition frequencies differ from each other by multiples of a small negative parameter α which characterizes the anharmonicity. In experiments using the circuit QED architecture, not only the transition between ground |g and the first excited |e state at frequency ω ge , but also transitions between higher lying energy levels can easily be addressed [30] and complex quantum states can be realized [31]. In particular, the second excited state |f , which is separated from |e by ω ef = ω ge + α, has been used widely for quantum gates [32][33][34][35], and plays an important role in our implementation of the cavity-assisted Raman processes in a circuit QED setting.…”

Section: Introductionmentioning

confidence: 99%

Microwave-induced amplitude- and phase-tunable qubit-resonator coupling in circuit quantum electrodynamics

et al. 2015

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In the circuit quantum electrodynamics architecture, both the resonance frequency and the coupling of superconducting qubits to microwave field modes can be controlled via external electric and magnetic fields to explore qubit -photon dynamics in a wide parameter range. Here, we experimentally demonstrate and analyze a scheme for tuning the coupling between a transmon qubit and a microwave resonator using a single coherent drive tone. We treat the transmon as a three-level system with the qubit subspace defined by the ground and the second excited states. If the drive frequency matches the difference between the resonator and the qubit frequency, a Jaynes-Cummings type interaction is induced, which is tunable both in amplitude and phase. We show that coupling strengths of about 10 MHz can be achieved in our setup, limited only by the anharmonicity of the transmon qubit. This scheme has been successfully used to generate microwave photons with controlled temporal shape [Pechal et al., Phys. Rev. X 4, 041010 (2014)] and can be directly implemented with superconducting quantum devices featuring larger anharmonicity for higher coupling strengths.

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Section: Introductionmentioning

confidence: 99%

Microwave-induced amplitude- and phase-tunable qubit-resonator coupling in circuit quantum electrodynamics

et al. 2015

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“…The three-tone microwave pulse irradiating the qudit is synthesized by an IQ-mixer modulating a carrier frequency of 6.700 GHz. Other techniques are identical to those described in previous works on multi-level Josephson phase qudits 25,26 . Time , consistent with Pythagorean dynamics.…”

Section: Methodsmentioning

confidence: 97%

Hidden two-qubit dynamics of a four-level Josephson circuit

et al. 2014

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Multi-level control of quantum coherence exponentially reduces communication and computation resources required for a variety of applications of quantum information science. However, it also introduces complex dynamics to be understood and controlled. These dynamics can be simplified and made intuitive by employing group theory to visualize certain four-level dynamics in a 'Bell frame' comprising an effective pair of uncoupled two-level qubits. We demonstrate control of a Josephson phase qudit with a single multi-tone excitation, achieving successive population inversions between the first and third levels and highlighting constraints imposed by the two-qubit representation. Furthermore, the finite anharmonicity of our system results in a rich dynamical evolution, where the two Bell-frame qubits undergo entangling-disentangling oscillations in time, explained by a Cartan gate decomposition representation. The Bell frame constitutes a promising tool for control of multi-level quantum systems, providing an intuitive clarity to complex dynamics.

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“…The Wigner function represents the full information of the states of the cavity field and can be measured via quantum state tomography [64]. The Wigner function of the cavity field has recently been measured in circuit QED systems [65,66]. To obtain the state of the cavity field, let us now trace out the qubit part of the density operator for the qubit-cavity compos-ite system using the formula…”

Section: Numerical Analysismentioning

confidence: 99%

Generating nonclassical photon states via longitudinal couplings between superconducting qubits and microwave fields

Zhao

Liu

et al. 2015

Phys. Rev. A

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Besides the conventional transverse couplings between superconducting qubits (SQs) and electromagnetic fields, there are additional longitudinal couplings when the inversion symmetry of the potential energies of the SQs is broken. We study nonclassical-state generation in a SQ which is driven by a classical field and coupled to a single-mode microwave field. We find that the classical field can induce transitions between two energy levels of the SQs, which either generate or annihilate, in a controllable way, different photon numbers of the cavity field. The effective Hamiltonians of these classical-field-assisted multiphoton processes of the singlemode cavity field are very similar to those for cold ions, confined to a coaxial RF-ion trap and driven by a classical field. We show that arbitrary superpositions of Fock states can be more efficiently generated using these controllable multiphoton transitions, in contrast to the single-photon resonant transition when there is only a SQ-field transverse coupling. The experimental feasibility for different SQs is also discussed.

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Direct Wigner Tomography of a Superconducting Anharmonic Oscillator

Cited by 48 publications

References 20 publications

Microwave-induced amplitude- and phase-tunable qubit-resonator coupling in circuit quantum electrodynamics

Microwave-induced amplitude- and phase-tunable qubit-resonator coupling in circuit quantum electrodynamics

Hidden two-qubit dynamics of a four-level Josephson circuit

Generating nonclassical photon states via longitudinal couplings between superconducting qubits and microwave fields

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