Unitary transformation and the dynamics of a three-level atom interacting with two quantized field modes

Alexanian, Moorad; Bose, S. K.

doi:10.1103/physreva.52.2218

Cited by 104 publications

(66 citation statements)

References 23 publications

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“…It is instructive to compare the tunable transmonresonator couplingg to the effective coupling g Λ = gΩe iφ /∆ between the two degenerate states of a Λ system obtained from the adiabatic elimination technique [23,25,28,39]. Most notably, the coupling strength for the transmon-resonator system is lower than that of the Λ system,g < g Λ .…”

Section: Calculating the Coupling Strengthgmentioning

confidence: 99%

“…The amplitude and phase tunability of the qubitresonator coupling strength can be achieved by a twophoton process, known as a cavity-assisted Raman process, which has been extensively studied for Λ-systems [23][24][25][26][27] and ladder-type (Ξ) systems [28]. Cavity-assisted Raman processes employ an external coherent drive with a time-dependent amplitude Ω cos (ω d t + φ) to induce an effective couplingg between the qubit and the resonator degrees of freedom.…”

Section: Introductionmentioning

confidence: 99%

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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: Calculating the Coupling Strengthgmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2015

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“…It is then possible to approximate the JC model by an effective one where the initially empty level has been adiabatically eliminated. In the appendix A I derive an effective JC model by transforming the Hamiltonian by an unitary operator [39,40]. The resulting Hamiltonian, to order O(g 2 /∆), becomes…”

Section: Generation Of Entangled States 1; Zero Detuningmentioning

confidence: 99%

Scheme for generating entangled states of two field modes in a cavity

Larson

2006

Journal of Modern Optics

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This paper considers a two-level atom interacting with two cavity modes with equal frequencies. Applying a unitary transformation, the system reduces to the analytically solvable Jaynes-Cummings model. For some particular field states, coherent and squeezed states, the transformation between the two bare basis's, related by the unitary transformation, becomes particularly simple. It is shown how to generate, the highly non-classical, entangled coherent states of the two modes, both in the zero and large detuning cases. An advantage with the zero detuning case is that the preparation is deterministic and no atomic measurement is needed. For the large detuning situation a measurement is required, leaving the field in either of two orthogonal entangled coherent states.

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“…9, where the fields are assumed driven. When the detuning ∆ in the figure is large, the upper level can be adiabatically eliminated [36] to give the interaction Hamiltonian (scaled units)…”

Section: The Problem Of Lossesmentioning

confidence: 99%

Level crossings in a cavity QED model

Larson

2006

Phys. Rev. A

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In this paper I study the dynamics of a two-level atom interacting with a standing wave field. When the atom is subjected to a weak linear force, the problem can be turned into a time dependent one, and the evolution is understood from the band structure of the spectrum. The presence of level crossings in the spectrum gives rise to Bloch oscillations of the atomic motion. Here I investigate the effects of the atom-field detuning parameter. A variety of different level crossings are obtained by changing the magnitude of the detuning, and the behaviour of the atomic motion is strongly affected due to this. I also consider the situation in which the detuning is oscillating in time and its impact on the atomic motion. Wave packet simulations of the full problem are treated numerically and the results are compared with analytical solutions given by the standard Landau-Zener and the three-level Landau-Zener models.

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Unitary transformation and the dynamics of a three-level atom interacting with two quantized field modes

Cited by 104 publications

References 23 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

Scheme for generating entangled states of two field modes in a cavity

Level crossings in a cavity QED model

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