arXiv subjects

Shu He

Publications and source records attributed to Shu He.

28 records · Page 2Linked to original sources

arXiv2015

Solution of the two-mode quantum Rabi model using extended squeezed states

The two-mode quantum Rabi model with bilinear coupling is studied using extended squeezed states. We derive $G$-functions for each Bargmann index $q$% . They share a common structure with the $G$-function of the one-photon and two-photon quantum Rabi models. The regular spectrum is given by zeros of the $G$-function while the conditions for the presence of doubly degenerate (exceptional) eigenvalues are obtained in closed form through the lifting property. The simple singularity structure of the $G$-function allows to draw conclusions about the distribution of eigenvalues along the real axis and to understand the spectral collapse phenomenon when the coupling reaches a critical value.

quant-ph↗

arXiv2015

Concise analytic solutions to the quantum Rabi model with two arbitrary qubits

Using extended coherent states, an analytical exact study has been carried out for the quantum Rabi model (QRM) with two arbitrary qubits in a very concise way. The $G$-functions with $2 \times 2$ determinants are generally derived. For the same coupling constants, the simplest $G$-function, resembling that in the one-qubit QRM, can be obtained. Zeros of the $G$-function yield the whole regular spectrum. The exceptional eigenvalues, which do not belong to the zeros of the $G$ function, are obtained in the closed form. The Dark states in the case of the same coupling can be detected clearly in a continued-fraction technique. The present concise solution is conceptually clear and practically feasible to the general two-qubit QRM and therefore has many applications.

quant-ph↗

arXiv2015

Exact solvability, non-integrability, and genuine multipartite entanglement dynamics of the Dicke model

In this paper, the finite size Dicke model of arbitrary number of qubits is solved analytically in an unified way within extended coherent states. For the $N=2k$ or $2k-1$ Dicke models ($k$ is an integer), the $G$-function, which is only an energy dependent $k \times k$ determinant, is derived in a transparent manner. The regular spectrum is completely and uniquely given by stable zeros of the $G$-function. The closed-form exceptional eigenvalues are also derived. The level distribution controlled by the pole structure of the $G$-functions suggests non-integrability for $N>1$ model at any finite coupling in the sense of recent criterion in literature. A preliminary application to the exact dynamics of genuine multipartite entanglement in the finite $N$ Dicke model is presented using the obtained exact solutions.

quant-ph↗

arXiv2014

Quantum phase transitions of the spin-boson model within multi-coherent-states

A variational approach based on the multi-coherent-state ansatz with asymmetric parameters is employed to study the ground state of the spin-boson model. Without any artificial approximations except for the finite number of the coherent states, we find the robust Gaussian critical behavior in the whole sub-Ohmic bath regime. The converged critical coupling strength can be estimated with the $1/N$ scaling, where $N $ is the number of the coherent states. It is strongly demonstrated the breakdown of the well-known quantum-to-classical mapping for $1/2<s<1$. In addition, the entanglement entropy displays more steep jump around the critical points for the Ohmic bath than the sub-Ohmic bath.

cond-mat.quant-gas↗

arXiv2014

Absence of collapse in quantum Rabi oscillations

We show analytically that the collapse and revival in the population dynamics of the atom-cavity coupled system under the rotating wave approximation (RWA), valid only at very weak coupling, is an artifact as the atom-cavity coupling is increased. Even the first-order correction to the RWA is able to bring about the absence of the collapse in the dynamics of atomic population inversion thanks to intrinsic oscillations resulting from the transitions between two levels with the same atomic quantum number. The removal of the collapse is valid for a wide range of coupling strengths which are accessible to current experimental setups. In addition, based on our analytical results that greatly improve upon the conventional RWA, even the strong-coupling power spectrum can now be explained with the help of the numerically exact energy levels.

quant-ph↗

arXiv2014

Quantum criticality of the sub-Ohmic spin-boson model within displaced Fock states

The spin-boson model is analytically studied using displaced Fock states (DFS) without discretization of the continuum bath. In the orthogonal displaced Fock basis, the ground-state wavefunction can be systematically improved in a controllable way. Interestingly, the zeroth-order DFS reproduces exactly the well known Silbey-Harris results. In the framework of the second-order DFS, the magnetization and the entanglement entropy are exactly calculated. It is found that the magnetic critical exponent $β$ is converged to $0.5$ in the whole sub-Ohmic bath regime $0<s<1$, compared with that by the exactly solvable generalized Silbey-Harris ansatz. It is strongly suggested that the system with sub-Ohmic bath is always above its upper critical dimension, in sharp contrast with the previous findings. This is the first evidence of the violation of the quantum-classical Mapping for $% 1/2<s<1$.

quant-ph↗

arXiv2014

Solutions to the quantum Rabi model with two equivalent qubits

Using extended coherent states, an analytically exact study has been carried out for the quantum Rabi model with two equivalent qubits. Compact transcendental functions of one variable have been derived leading to exact solutions. The energy spectrum is clearly identified and analyzed. Also obtained analytically is the necessary and sufficient conditions for the occurrence of isolated exceptional solutions, which are not doubly degenerate as in the one-qubit quantum Rabi model.

quant-ph↗

arXiv2012

Exact solvability of the quantum Rabi models within Bogoliubov operators

The quantum Rabi model can be solved exactly by the Bargmann transformation from real coordinate to complex variable recently [Phys. Rev. Lett. \textbf{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 two-photon 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.

quant-ph↗

arXiv2012

Unified analytical treatments to qubit-oscillator systems

An effective scheme within two displaced bosonic operators with equal positive and negative displacements is extended to study qubit-oscillator systems analytically in an unified way. Many previous analytical treatments, such as generalized rotating-wave approximation (GRWA) [Phys. Rev. Lett. 99, 173601 (2007)] and an expansion in the qubit tunneling matrix element in the deep strong coupling regime [Phys. Rev. Lett. 105, 263603 (2010)] can be recovered straightforwardly in the present scheme. Moreover, further improving GRWA and extension to the finite-bias case are implemented easily. The analytical expressions are then derived explicitly and uniquely, which work well in a wide range of the coupling strengthes, detunings, and static bias including the recent experimentally accessible parameters.

quant-ph↗

arXiv2012

Jaynes-Cummings model: What emerges first beyond the rotating-wave approximation?

The Jaynes-Cummings model without the rotating-wave approximation can be solved exactly by extended Swain's ansatz with the conserved parity. The analytical approximations are then performed at different levels. The well-known rotating-wave approximation is naturally covered in the present zero and first approximations. The effect of the counter rotating-wave term emerges clearly in the second order approximation. The concise analytical expressions are given explicitly and can be applicable up to the ultra-strong coupling regime. The preliminary application to the vacuum Rabi splitting is shown to be very successful.

quant-ph↗