arXiv subjects

Yu-Yu Zhang

Publications and source records attributed to Yu-Yu Zhang.

At least 37 records · Page 2Linked to original sources

arXiv2019

Powerful harmonic charging in quantum batteries

We consider a classical harmonic driving field as the energy charger for the quantum batteries, which consist of an ensemble of two-level atoms. The maximum stored energy and the final state are derived analytically with the optimal driving frequency. At the end of charging procedure, each of atoms is in the upper state and the batteries are charging completely, which exhibits a substantial improvement over the square-wave charger. Involving the interatomic correlations, we find that the repulsive couplings show an advantage in achieving fully charging with shorter charging period. However, the attractive interactions induce a negative effects on the charging, since the ground state undergoes a quantum phase transition from a separable state to a doubly degenerate state. Approaching to the phase transition regime, the maximum stored energy drops sharply from the fully-charging value. The phase transition favors to suppress the charging of the battery and prevents the final state to be a separable state due to quantum fluctuations in our quantum batteries.

quant-ph↗

arXiv2019

Generalized coherent-squeezed-state expansion for the quantum Rabi model

We develop a systematic variational coherent-squeezed-state expansion for the ground state of the quantum Rabi model, which includes an additional squeezing effect with comparisons to previous coherent-state approach. For finite large ratio between the atomic and field frequency, the essential feature of the ground-state wave function in the super-radiant phase appears, which has a structure of two delocalized wake packets. The single-peaked wave function with one coherent-squeezed state works well even around the critical regime, exhibiting the advantage over the coherent-state method. As the coupling increases to form strong correlations physics in the vicinity of phase transition, we develop an improved wave function with a structure of two Gaussian wave packets, which is a linear superposition of two coherent-squeezed state. The ground-state energy and the average photon number agree well with numerical ones even in the strong-correlated regimes, exhibiting a substantial improvement over the coherent-state expansion. The advantage of the coherent-squeezed-state expansion lies in the inclusion of the second coherent-squeezed state and the additional squeezed deformation of the wave function, providing a useful tool for multi-modes spin-boson coupling systems of greater complexity.

quant-ph↗

arXiv2018

Finite-size scaling analysis in the two-photon Dicke model

The Hamiltonian of the two-photon Dicke model is diagonalized for the normal phase and super-radiant phase beyond the mean-field method respectively, giving the critical coupling strength. Besides a spectral collapse, the super-radiant phase transition is presented by the vanishing of the excitation energy, which is lower than the mean-field results. Finite-size scaling exponents for the ground-state energy and the atomic angular momentum are analytically derived from scaling hypothesis, belonging to the same scaling universality of the one-photon Dicke model.

quant-ph↗

arXiv2017

Analytical solutions by squeezing to the anisotropic Rabi model in the nonperturbative deep-strong coupling regime

A novel, unexplored nonperturbative deep-strong coupling (npDSC) achieved in superconducting circuits has been studied in the anisotropic Rabi model by the generalized squeezing rotating-wave approximation (GSRWA). Energy levels are evaluated analytically from the reformulated Hamiltonian and agree well with numerical ones under a wide range of coupling strength. Such improvement ascribes to deformation effects in the displaced-squeezed state presented by the squeezed momentum variance, which are omitted in the previous displaced state. The population dynamics confirm the validity of our approach for the npDSC strength. Our approach paves a way to the exploration of analysis in qubit-oscillator experiments for the npDSC strength by the displaced-squeezed state.

quant-ph↗

arXiv2016

Generalized squeezing rotating-wave approximation to the isotropic and anisotropic Rabi model in the ultrastrong-coupling regime

Generalized squeezing rotating-wave approximation (GSRWA) is proposed by employing both the displacement and the squeezing transformations. A solvable Hamiltonian is reformulated in the same form as the ordinary RWA ones. For a qubit coupled to oscillators experiment, a well-defined Schrödinger-cat-like entangled state is given by the displaced-squeezed oscillator state instead of the original displaced state. For the isotropic Rabi case, the mean photon number and the ground-state energy are expressed analytically with additional squeezing terms, exhibiting a substantial improvement of the GSRWA. And the ground-state energy in the anisotropic Rabi model confirms the effectiveness of the GSRWA. Due to the squeezing effect, the GSRWA improves the previous methods only with the displacement transformation in a wide range of coupling strengths even for large atom frequency.

quant-ph↗

arXiv2016

Analytical solutions and genuine multipartite entanglement of the three-qubit Dicke model

We present analytical solutions to three qubits and a single-mode cavity coupling system beyond the rotating-wave approximation (RWA). The zero-th order approximation gives correct solutions when the qubits are far detuned from the cavity. The first order approximation, called generalized rotating-wave approximation (GRWA), produces an effective solvable Hamiltonian with the same form as the ordinary RWA one and exhibits substantial improvements of energy levels over the RWA even on resonance. Based on these analytical eigen-solutions, we study both the bipartite entanglement and genuine multipartite entanglement (GME). The dynamics of the concurrence and the GME using the GRWA are in consistent with the numerical ones. Interestingly, the well known sudden death of entanglement occurs in the bipartite entanglement dynamics but not in GME dynamics.

quant-ph↗

arXiv2015

Large-N scaling behavior of the quantum fisher information in the Dicke model

Quantum Fisher information (QFI) of the reduced two-atom state is employed to capture the quantum criticality of the superradiant phase transition in the Dicke model in the infinite size and finite-$N$ systems respectively. The analytical expression of the QFI of its ground state is evaluated explicitly. And finite-size scaling analysis is performed with the large accessible system size due to the effective bosonic coherent-state technique. We also investigate the large-size scaling behavior of the scaled QFI of the reduced $N$-atom state and show the accurate exponent.

quant-ph↗

arXiv2014

Generalized rotating-wave approximation to the two-qubit and cavity coupling system

The generalized rotating-wave approximation (GRWA) is presented for the two-qubit and cavity coipling system . The analytical expressions in the zeroth order approximation recover the previous adiabatic ones. The counterrotating-wave terms can be eliminated by performing the first order corrections. An effective solvable Hamiltonian with the same form as the ordinary RWA one are then obtained, giving a significantly accurate eigenvalues and eigenstates. Energy levels in the present GRWA are in accordant with the numerical exact diagonalization ones in the a wide range of coupling strength. The atomic population inversion in the GRWA is in quantitative agreement with the numerical results for different detunings in the ultrastrong coupling regime.

quant-ph↗

arXiv2013

Generalized rotating-wave approximation to biased qubit-oscillator systems

The generalized rotating-wave approximation with counter-rotating interactions has been applied to a biased qubit-oscillator system. Analytical expressions are explicitly given for all eigenvalues and eigenstates. For a flux qubit coupled to superconducting oscillators, spectra calculated by our approach are in excellent agreement with experiment. Calculated energy levels for a variety of biases also agree well with those obtained via exact diagonalization for a wide range of coupling strengths. Dynamics of the qubit has also been examined, and results lend further support to the validity of the analytical approximation employed here. Our approach can be readily implemented and applied to superconducting qubit-oscillator experiments conducted currently and in the near future with a biased qubit and for all accessible coupling strengths.

quant-ph↗

arXiv2012

Quantum correlations in the collective spin systems

Quantum and classical pairwise correlations in two typical collective spin systems (i.e., the Dicke model and the Lipkin-Meshkov-Glick model) are discussed. These correlations in the thermodynamical limit are obtained analytically and in a finite-size system are calculated numerically. Large-size scaling behavior for the quantum discord itself is observed, which has never been reported in another critical system. A logarithmic diverging behavior for the first derivative of the quantum discord is also found in both models, which might be universal in the second-order quantum phase transition. It is suggested that the pronounced maximum or minimum of first derivative of quantum discord signifies the critical point. Comparisons between the quantum discord and the scaled concurrence are performed. It is shown that the quantum discord is very small in one phase and robust in the other phase, while the scaled concurrence shows maximum at the critical point and decays rapidly when away from the the critical point.

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↗

arXiv2011

Jaynes-Cummings model:Counter rotating effect on the vacuum Rabi splitting and atom-cavity dynamics

he effect of the counter-rotating terms in the Jaynes-Cummings model is investigated with an extended coherent-state approach. The counter-rotating terms greatly modify the vacuum Rabi splitting. Two peaks with different heights in the weak coupling regime and more than two peaks in the intermediate coupling regime are predicted. The collapses and revivals in the evolution of the atomic population inversion disappear in the intermediate coupling regime, but reappear in the strong coupling regime. This reappearance is similar to that under the rotating-wave approximation, attributed to the summation of periodic cosine functions of the evolution.

quant-ph↗

arXiv2010

Solutions to the Jaynes-Cummings model without the rotating-wave approximation

By using extended bosonic coherent states, the solution to the Jaynes-Cummings model without the rotating-wave approximation can be mapped to that of a polynomial equation with a single variable. The solutions to this polynomial equation can give all eigenvalues and eigenfunctions of this model with all values of the coupling strength and the detuning exactly, which can be readily applied to recent circuit quantum electrodynamic systems operating in the ultra-strong coupling regime.

quant-ph↗

arXiv2010

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

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.

quant-ph↗

arXiv2010

Quantum Phase Transition in the Sub-Ohmic Spin-Boson Model: Extended Coherent-state Approach

We propose a general extended coherent state approach to the qubit (or fermion) and multi-mode boson coupling systems. The application to the spin-boson model with the discretization of a bosonic bath with arbitrary continuous spectral density is described in detail, and very accurate solutions can be obtained. The quantum phase transition in the nontrivial sub-Ohmic case can be located by the fidelity and the order-parameter critical exponents for the bath exponents $s<1/2$ can be correctly given by the fidelity susceptibility, demonstrating the strength of the approach.

cond-mat.quant-gas↗

arXiv2009

Large-N scaling behavior of the ground-state energy and fidelity in the Dicke Model

Within the numerically exact solution to the Dicke model proposed previously, we study the quantum criticality in terms of the ground-state (GS) energy, fidelity, and the order parameter. The finite size scaling analysis for the average fidelity susceptibility (FS) and second derivative of GS energy are performed. The correlation length exponent is obtained to be $ν=2/3$, which is the same as that in Lipkin-Meshkov-Glick model obtained previously, suggesting the same universality. It is observed that average FS and second derivative of GS energy show similar critical behavior, demonstrating the intrinsic relation in the Dicke model. The scaling behavior for the order parameter and the singular part of the GS energy at the critical point are also analyzed and the obtained exponents are consistent with the previous scaling hypothesis in 1/N expansion scheme.

quant-ph↗

arXiv2009

Quantum phase transition in the one-dimensional period-two and uniform compass model

Quantum phase transition in the one-dimensional period-two and uniform quantum compass model are studied by using the pseudo-spin transformation method and the trace map method. The exact solutions are presented, the fidelity, the nearest-neighbor pseudo-spin entanglement, spin and pseudo-spin correlation functions are then calculated. At the critical point, the fidelity and its susceptibility change substantially, the gap of pseudo-spin concurrence is observed, which scales as $1/N$ (N is system size). The spin correlation functions show smooth behavior around the critical point. In the period-two chain, the pseudo-spin correlation functions exhibit a oscillating behavior, which is absent in the unform chain. The divergent correlation length at the critical point is demonstrated in the general trend for both cases.

cond-mat.str-el↗

arXiv2009

Berry Phase and Fidelity in the Dicke model with $A^{2}$ term

The instability, so-called the quantum-phase-like transition, in the Dicke model with a rotating-wave approximation for finite $N$ atoms is investigated in terms of the Berry phase and the fidelity. It can be marked by the discontinuous behavior of these quantities as a function of the atom-field coupling parameter. Involving an additional field $A^{2}$ term, it is observed that the instability is not eliminated beyond the characteristic atom-field coupling parameter even for strong interaction of the bosonic fields, contrarily to the previous studies.

quant-ph↗