Theory of Spectrum in Qubit-Oscillator Systems in the Ultrastrong Coupling Regime

Chen, Qing-Hu; Li, Lei; Liu, Tao; Wang, Kelin

doi:10.48550/arxiv.1007.1747

Cited by 9 publications

(13 citation statements)

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“…In this paper, without the use of any extra conditions, like analyticity of the eigenfunction in Bargmann representation, we alternatively re-derive the same transcendental functions as in Ref. [13] quantum mechanically within the extended coherent stats [15,16]. Both zero bias and biased QRM can be treated simultaneously.…”

Section: Introductionmentioning

confidence: 99%

Exact solvability of the quantum Rabi model using Bogoliubov operators

et al. 2012

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The quantum Rabi model can be solved exactly by the Bargmann transformation from real coordinate to complex variable recently [Phys. Rev. Lett. 107, 100401 (2011)]. By the extended coherent states, we recover this solution in an alternative simpler and perhaps more physical way without uses of any extra conditions, like Bargmann conditions. In the same framework, the twophoton Rabi model are solved exactly by extended squeeze states. Transcendental functions have been derived with the similar form as those in one-photon model. Both extended coherent states and squeeze states are essentially Fock states in the space of the corresponding Bogoliubov operators. The present approach could be easily extended to study the exact solvability or integrability of various spin-boson systems with multi-level, even multi-mode.

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Section: Introductionmentioning

confidence: 99%

Exact solvability of the quantum Rabi model using Bogoliubov operators

et al. 2012

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“…Most works on the modified Dicke model are limited to the rotating-wave approximation. With the progress of the fabrication, the artificial atoms may interact very strongly with on-chip resonant circuits [8,9,11,12], the rotating-wave approximation can not describe well the strong coupling regime [13], so the numerically exact solution to the modified Dicke model without rotating-wave approximation is also of considerable significance and highly called for.…”

Section: Introductionmentioning

confidence: 99%

Quantum phase transitions in coupled two-level atoms in a single-mode cavity

et al. 2010

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The dipole-coupled two-level atoms(qubits) in a single-mode resonant cavity is studied by extended bosonic coherent states. The numerically exact solution is presented. For finite systems, the first-order quantum phase transitions occur at the strong interatomic interaction. Similar to the original Dicke model, this system exhibits a second-order quantum phase transition from the normal to the superradiant phases. Finite-size scaling for several observables, such as the average fidelity susceptibility, the order parameter, and concurrence are performed for different interatomic interactions. The obtained scaling exponents suggest that interatomic interactions do not change the universality class.

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“…Nowadays, solid-state semiconductor [13] or superconductor systems [14][15][16][17][18][19][20] have allowed the advent of the ultrastrong coupling (USC) regime, where the coupling strength is comparable or larger than appreciable fractions of the mode frequency: g/ω > ∼ 0.1. In this regime, the RWA breaks down and the model becomes analytically unsolvable, although some limits can be explored [21][22][23][24][25]. Confident of the impressive fast development of current technology, one could explore further regimes where the rate between the coupling strength and oscillator frequency could reach g/ω > ∼ 1, here called deep SC (DSC) regime.…”

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confidence: 99%

Deep Strong Coupling Regime of the Jaynes-Cummings Model

et al. 2010

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We study the quantum dynamics of a two-level system interacting with a quantized harmonic oscillator in the deep strong coupling regime (DSC) of the Jaynes-Cummings model, that is, when the coupling strength g is comparable or larger than the oscillator frequency ω (g/ω > ∼ 1). In this case, the rotating-wave approximation cannot be applied or treated perturbatively in general. We propose an intuitive and predictive physical frame to describe the DSC regime where photon number wavepackets bounce back and forth along parity chains of the Hilbert space, while producing collapse and revivals of the initial population. We exemplify our physical frame with numerical and analytical considerations in the qubit population, photon statistics, and Wigner phase space.The interaction between a two-level system and a harmonic oscillator is ubiquitous in different physical setups, ranging from quantum optics to condensed matter and applications to quantum information. Typically, due to the parameter accessibility of most experiments, the rotating-wave approximation (RWA) can be applied producing a solvable dynamics called the Jaynes-Cummings (JC) model [1]. In this case, Rabi oscillations inside the JC doublets or collapses and revivals of the system populations [2] are paradigmatic examples of the intuitive physics behind the JC dynamics. To achieve these and other phenomena in the lab, the strong coupling (SC) regime is required, that is, the qubit-oscillator coupling has to be comparable or larger than all decoherence rates. This model accurately describes the dynamics of cavity QED [3,4], trapped ion experiments [5], and several setups in mesoscopic physics, where the qubit-oscillator model is essential in modeling superconducting qubits [6] with either coplanar transmission lines [7][8][9][10] or nanomechanical resonators [11,12]. Nowadays, solid-state semiconductor [13] or superconductor systems [14][15][16][17][18][19][20] have allowed the advent of the ultrastrong coupling (USC) regime, where the coupling strength is comparable or larger than appreciable fractions of the mode frequency: g/ω > ∼ 0.1. In this regime, the RWA breaks down and the model becomes analytically unsolvable, although some limits can be explored [21][22][23][24][25]. Confident of the impressive fast development of current technology, one could explore further regimes where the rate between the coupling strength and oscillator frequency could reach g/ω > ∼ 1, here called deep SC (DSC) regime. This unusual regime, yet to be experimentally explored, is the focus of our current efforts. In this letter, we introduce a rigorous and intuitive description of the DSC regime of the JC model, providing an insightful picture where photon number wavepackets propagate coherently along two independent parity chains of states. In this way, the Hilbert space splits in two independent chains, exhibiting a comprehensible collapse-revival pattern of the system populations.We consider the Jaynes-Cummings Hamiltonian without the RWA, also called Rabi Hamiltonian, desc...

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Theory of Spectrum in Qubit-Oscillator Systems in the Ultrastrong Coupling Regime

Cited by 9 publications

References 0 publications

Exact solvability of the quantum Rabi model using Bogoliubov operators

Exact solvability of the quantum Rabi model using Bogoliubov operators

Quantum phase transitions in coupled two-level atoms in a single-mode cavity

Deep Strong Coupling Regime of the Jaynes-Cummings Model

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