Squeezing based analytical variational method for the biased quantum Rabi model in the ultrastrong coupling regime

Xie, Weijie; Mao, Bin-Bin; Li, Guangzhuo; Wang, Weihang; Sun, Chen; Wang, Yimin; You, Wen-Long; Liu, Maoxin

doi:10.1088/1751-8121/ab4b7a

Cited by 8 publications

(14 citation statements)

References 51 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is lengthy but rather straighforward to expand the hyperbolic functions as the even and odd part of the exponential (see Xie et al [27] but beware of typos)…”

Section: The Generalized Rwa Effective Hamiltonianmentioning

confidence: 99%

“…Their spectra, average photon number, population inversion and number of excitations are obtained and compared both analytically and numerically in subsections III A, III B, and III C. We also compare our result with the so called generalized rotating wave Hamiltonian (GRWA) obtained by Irish [25] in the deep strong coupling case (subsection III D). This regime is defined by large values of the coupling, g/ω ≈ 1 and beyond, but the numerical evidence [26][27][28] shows that this approach gives good results at lower couplings too. Therefore comparison against it is relevant.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Effective Hamiltonians in the Quantum Rabi Problem

Gartner,

Moldoveanu

2021

Preprint

View full text Add to dashboard Cite

We revisit the theoretical description of the ultrastrong light-matter interaction in terms of exactly solvable effective Hamiltonians. A perturbative approach based on polaronic and spindependent squeezing transformations provides an effective Hamiltonian for the quantum Rabi model up to the second order in the expansion parameter. The model consistently includes both rotating and counter-rotating terms, going therefore beyond the rotating wave approximation. Analytical and numerical results show that the proposed Hamiltonian performs better than the Bloch-Siegert model when calculating operator averages (e.g. the mean photon number and number of excitations). This improvement is due to a refined calculation of the dressed states within the present model. Regarding the frequency shift induced by the qubit-photon interaction, we find a different sign from the Bloch-Siegert value. This influences the eigenstates structure in a non-trivial way and ensures the correct calculation of the number of excitations associated to a given dressed state. As a consistency check, we show that the exactly solvable independent boson model is reproduced as a special limit case of the perturbative Hamiltonian.

show abstract

“…It is lengthy but rather straighforward to expand the hyperbolic functions as the even and odd part of the exponential (see Xie et al [27] but beware of typos)…”

Section: The Generalized Rwa Effective Hamiltonianmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effective Hamiltonians in the Quantum Rabi Problem

Gartner,

Moldoveanu

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The GRWA, as well as its further generalizations, have been applied to other light-matter interaction models. The example of interest here, and most relevant to the current cQED experiments, is the application to the asymmetric quantum Rabi model (AQRM) [34][35][36]. The AQRM is a generalization of the QRM with a bias term [10,11,13,14,[37][38][39][40], which naturally appears in the cQED systems to describe qubits with an asymmetric potential such as for flux qubits [7,9,[22][23][24].…”

Section: Introductionmentioning

confidence: 99%

“…The AQRM is a generalization of the QRM with a bias term [10,11,13,14,[37][38][39][40], which naturally appears in the cQED systems to describe qubits with an asymmetric potential such as for flux qubits [7,9,[22][23][24]. The approximation methods for the AQRM may be classified into the GRWA [34], the GVM [35] and the GSRWA [36], following the treatment of the QRM. The work by arXiv:2006.08913v1 [quant-ph] 16 Jun 2020…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonorthogonal-qubit-state expansion for the asymmetric quantum Rabi model

Ferri

Batchelor

2021

Phys. Rev. A

View full text Add to dashboard Cite

We present a physically motivated variational wave function for the ground state of the asymmetric quantum Rabi model (AQRM). The wave function is a weighted superposition of squeezed coherent states entangled with non-orthogonal qubit states, and relies only on three variational parameters. The variational expansion describes the ground state remarkably well in almost all parameter regimes, especially with arbitrary bias. We use the variational result to calculate various relevant physical observables of the ground state, and make a comparison with existing approximations and the exact solution. The results show that the variational expansion is a significant improvement over the existing approximations for the AQRM.

show abstract

Ground-state phase diagram, symmetries, excitation spectra and finite-frequency scaling of the two-mode quantum Rabi model

2023

View full text Add to dashboard Cite

We investigate two-mode quantum Rabi model (QRM) describing the interaction between a twolevel atom and a two-mode cavity field. The quantum phase transitions are found when the ratio η of transition frequency of atom to frequency of cavity field approaches infinity. We apply SchriefferWolff (SW) transformation to derive the low-energy effective Hamiltonian of the two-mode QRM, thus yielding the critical point and rich phase diagram of quantum phase transitions. The phase diagram consists of four regions: a normal phase, an electric superradiant phase, a magnetic superradiant phase and an electromagnetic superradiant phase. The quantum phase transition between the normal phase and the electric (magnetic) superradiant phase is of second order and associated with the breaking of the discrete Z 2 symmetry. On the other hand, the phase transition between the electric superradiant phase and the magnetic superradiant phase is of first order and relating to the breaking of the continuous U(1) symmetry. Several important physical quantities, for example the excitation energy and average photon number in the four phases, are derived. We find that the excitation spectra exhibit the Nambu-Goldstone mode. We calculate analytically the higher-order correction and finite-frequency exponents of relevant quantities. To confirm the validity of the lowenergy effective Hamiltonians analytically derived by us, the finite-frequency scaling relation of the averaged photon numbers are calculated by numerically diagonalizing the two-mode quantum Rabi Hamiltonian.

show abstract

Squeezing based analytical variational method for the biased quantum Rabi model in the ultrastrong coupling regime

Cited by 8 publications

References 51 publications

Effective Hamiltonians in the Quantum Rabi Problem

Effective Hamiltonians in the Quantum Rabi Problem

Nonorthogonal-qubit-state expansion for the asymmetric quantum Rabi model

Ground-state phase diagram, symmetries, excitation spectra and finite-frequency scaling of the two-mode quantum Rabi model

Contact Info

Product

Resources

About