Unified analytical treatments of qubit—oscillator systems

He, Song; Zhang, Yuyu; Chen, Qing-Hu; Xue-Zao, Ren; Liu, Tao; Wang, Kelin

doi:10.1088/1674-1056/22/6/064205

Cited by 12 publications

(9 citation statements)

References 53 publications

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“…In 2007, Irish proposed the so-called general rotating wave approximation (GRWA) [27], which does succeed in presenting the correct structure of the energy spectrum over a large parameter regime. It also provides a framework to analytically treat many models which are cousins of the quantum Rabi model [28,29,30,31,32,33,34,35,36,37,38,39,40,41,42].…”

Section: Introductionmentioning

confidence: 99%

An analytical variational method for the biased quantum Rabi model in the ultra-strong coupling regime

Mao

Liu

et al. 2018

Chinese Phys. B

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An analytical variational method for the ground state of the biased quantum Rabi model in the ultra-strong coupling regime is presented. This analytical variational method can be obtained by a unitary transformation or alternatively by assuming the form of ground state wave function. The key point of the method is to introduce a variational parameter λ, which can be determined by minimizing the energy functional. Using this method, we calculate physical observables with high accuracy in comparison with the numerical exact one. Our method evidently improves the results from the widely used general rotating-wave approximation (GRWA) in both qualitative and quantitative ways.

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Section: Introductionmentioning

confidence: 99%

An analytical variational method for the biased quantum Rabi model in the ultra-strong coupling regime

Mao

Liu

et al. 2018

Chinese Phys. B

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“…Recently, the study of superconducting qubit-oscillators in quantum computing systems with time-dependent parameters attracted considerable interest in the community of physics and information science [5][6][7][8][9]. In general, a high ability of computation with a tremendous speed can be achieved for particular mathematical problems from quantum computation on the basis of new paradigms known as superposition and entanglement.…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian Dynamics and Adiabatic Invariants for Time-Dependent Superconducting Qubit-Oscillators and Resonators in Quantum Computing Systems

Choi¹

2015

Advances in Mathematical Physics

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An adiabatic invariant, which is a conserved quantity, is useful for studying quantum and classical properties of dynamical systems. Adiabatic invariants for time-dependent superconducting qubit-oscillator systems and resonators are investigated using the Liouville-von Neumann equation. At first, we derive an invariant for a simple superconducting qubit-oscillator through the introduction of its reduced Hamiltonian. Afterwards, an adiabatic invariant for a nanomechanical resonator linearly interfaced with a superconducting circuit, via a coupling with a time-dependent strength, is evaluated using the technique of unitary transformation. The accuracy of conservation for such invariant quantities is represented in detail. Based on the results of our developments in this paper, perturbation theory is applicable to the research of quantum characteristics of more complicated qubit systems that are described by a time-dependent Hamiltonian involving nonlinear terms.

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“…that can be either up or down, creating a spin-1/2 system. These systems generally allow coupling strengths up to g j /ω c ≃ 0.1 in the so-called ultrastrong coupling regime, or the qubit transition frequency far-detuned from the field frequency [11][12][13][14][15][16][17][18][19][20][21][22][23][24]. An adiabatic approximation approach [15] was proposed to treat the parameter regime outside the nearresonance and weak-coupling assumption of RWA based * Electronic address: ybzhang@sxu.edu.cn on the displaced oscillator basis.…”

Section: Introductionmentioning

confidence: 99%

Tavis-Cummings model beyond the rotating wave approximation: Inhomogeneous coupling

Mao¹,

Huai²,

Zhang³

2014

Preprint

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We present the analytical solution of the Tavis-Cummings (TC) model for more than one qubit inhomogeneously coupled to a single mode radiation field beyond the rotating-wave approximation (RWA). The significant advantage of the displaced oscillator basis enables us to apply the same truncation techniques adopted in the single qubit Jaynes-Cummings (JC) model to the multiple qubits system. The derived analytical spectrum match perfectly the exact diagonalization numerical solutions of the inhomogeneous TC model in the parameter regime where the qubits transition frequencies are far off-resonance with the field frequency and the interaction strengths reach the ultra-strong coupling regime. The two-qubit TC model is quasi-exactly solvable because part of the spectra can be determined exactly in the homogeneous coupling case with two identical qubits or with symmetric(asymmetric) detuning. By means of the fidelity of quantum states we identify several nontrivial level crossing points in the same parity subspace, which implies that homogeneous coupled two-qubit TC model with ω1 = ω2 or ω1 ± ω2 = 2ωc is integrable. We further explore the time evolution of the qubit's population inversion and the entanglement behavior taking two qubits as an example. The analytical methods provide unexpectedly accurate results in describing the dynamics of the qubit in the present experimentally accessible coupling regime, showing that the collapse-revival phenomena emerge, survive, and are finally destroyed when the coupling strength increases beyond the ultra-strong coupling regime. The inhomogeneous coupling system exhibits new dynamics, which are different from homogeneous coupling case. The suggested procedure applies readily to the multiple qubits system such as the GHZ state entanglement evolution and quantum entanglement between a single photon and superconducting qubits of particular experiment interest.

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Unified analytical treatments of qubit—oscillator systems

Cited by 12 publications

References 53 publications

An analytical variational method for the biased quantum Rabi model in the ultra-strong coupling regime

An analytical variational method for the biased quantum Rabi model in the ultra-strong coupling regime

Hamiltonian Dynamics and Adiabatic Invariants for Time-Dependent Superconducting Qubit-Oscillators and Resonators in Quantum Computing Systems

Tavis-Cummings model beyond the rotating wave approximation: Inhomogeneous coupling

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