arXiv subjects

J. -Q. Liang

Publications and source records attributed to J. -Q. Liang.

At least 19 recordsLinked to original sources

arXiv2025

Macroscopic quantum states, quantum phase transition for $N$ three-level atoms in an optical cavity -- Gauge principle and non-Hermitian Hamiltonian

We study in this paper the quantum phase transition (QPT) from normal phase (NP) to superradiant phase (SP) for $N$ three-level atoms in a single-mode optical cavity for both Hermitian and non Hermitian Hamiltonians, where the $Ξ$-type three-level atom is described by spin-$1$ pseudo-spin operators. The long standing gauge-choice ambiguity of $\mathbf{A\cdot p}$ and $\mathbf{d\cdot E}$ called respectively the Coulomb and dipole gauges is resolved by the time-dependent gauge transformation on the Schrödinger equation. Both $\mathbf{A\cdot p}$ and $\mathbf{d\cdot E}$ interactions are included in the unified gauge, which is truly gauge equivalent to the minimum coupling principle. The Coulomb and dipole interactions are just the special cases of unified gauge. Remarkably three interactions lead to the same results under the resonant condition of field-atom frequencies, while significant difference appears in red and blue detunings. The QPT is analyzed in terms of spin coherent-state variational method, which indicates the abrupt changes of energy spectrum, average photon number as well as the atomic population at the critical point of interaction constant. Crucially, we reveal the sensitive dependence on the initial optical-phase, which is particularly useful to test the validity of three gauges experimentally. The non-Hermitian atom-field interaction results in the exceptional point (EP), beyond which the semiclassical energy function becomes complex. However the energy spectrum of variational ground state is real in the absence of EP, and does not become complex. The superradiant state is unstable due to the non-Hermitian interaction induced photon-number loss. Thus only the NP exists in the non-Hermitian Dicke Model Hamiltonian.

quant-ph↗

arXiv2025

Quantum mechanics of inverted potential well -- Hermitian Hamiltonian with imaginary eigenvalues, quantum-classical correspondence

We in this paper study the quantization of a particle in an inverted potential well. The Hamiltonian is Hermitian, while the potential is unbounded below. Classically the particle moves away acceleratingly from the center of potential top. The existing eigenstates must be unstable with imaginary eigenvalues, which characterize the decay rate of states. We solve the Hamiltonian problem of inverted potential well by the algebraic method with imaginary-frequency raising and lowering boson operators similar to the normal oscillator case. The boson number operator is non-Hermitian, while the integer-number eigenvalues are, of course, real. Dual sets of eigenstates, denoted by "bra" and "ket", are requested corresponding respectively to the complex conjugate number-operators. Orthonormal condition exists between the "bra" and "ket" states. We derive a spatially non-localized generating function, from which $n$-th eigenfunctions can be generated by the raising operators in coordinate representation. The "bra" and "ket" generating functions are mutually normalized with the imaginary integration measure. The probability density operators defined between the "bra" and "ket" states are non-Hermitian invariants, which lead to the Schrődinger equations respectively for the "bra" and "ket" states. While probabilities of "bra" and "ket" states themselves are not conserved quantities because of the decay. The imaginary-frequency boson coherent states are defined as eigenstates of lowering operators. The minimum uncertainty relation is proved explicitly in the coherent states. Finally the probability average of Heisenberg equation in the coherent states is shown precisely in agreement with the classical equation of motion. The quantum-classical correspondence exists in the imaginary eigenvalue system.

quant-ph↗

arXiv2025

Imaginary eigenvalues of Hermitian Hamiltonian with an inverted potential well and transition to the real spectrum at exceptional point by a non-Hermitian interaction

We in this paper study the hermiticity of Hamiltonian and energy spectrum for the SU(1; 1) systems. The Hermitian Hamiltonian can possess imaginary eigenvalues in contrast with the common belief that hermiticity is a suffcient condition for real spectrum. The imaginary eigenvalues are derived in algebraic method with imaginary-frequency boson operators for the Hamiltonian of inverted potential well. Dual sets of mutually orthogonal eigenstates are required corresponding respectively to the complex conjugate eigenvalues. Arbitrary order eigenfunctions seen to be the polynomials of imaginary frequency are generated from the normalized ground-state wave functions, which are spatially non localized. The Hamiltonian including a non-Hermitian interaction term can be converted by similarity transformation to the Hermitian one with an effective potential of reduced slope, which is turnable by the interaction constant. The transformation operator should not be unitary but Hermitian different from the unitary transformation in ordinary quantum mechanics. The effective potential vanishes at a critical value of coupling strength called the exceptional point, where all eigenstates are degenerate with zero eigenvalue and transition from imaginary to real spectra appears. The SU(1; 1) generator $\widehat{S}_{z}$ with real eigenvalues determined by the commutation relation of operators, however, is non-Hermitian in the realization of imaginay-frequency boson operators. The classical counterpart of the quantum Hamiltonian with non-Hermitian interaction is a complex function of the canonical variables. It becomes by the canonical transformation of variables a real function indicating exactly the one to one quantum-classical correspondence of Hamiltonians.

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arXiv2022

Generalized gauge transformation with $PT$-symmetric non-unitary operator and classical correspondence of non-Hermitian Hamiltonian for a periodically driven system

We in this paper demonstrate that the $PT$-symmetric non-Hermitian Hamiltonian for a periodically driven system can be generated from a kernel Hamiltonian by a generalized gauge transformation. The kernel Hamiltonian is Hermitian and static, while the time-dependent transformation operator has to be $PT$ symmetric and non-unitary in general. Biorthogonal sets of eigenstates appear necessarily as a consequence of non-Hermitian Hamiltonian. We obtain analytically the wave functions and associated non-adiabatic Berry phase $γ_{n}$ for the $n$th eigenstate. The classical version of the non-Hermitian Hamiltonian becomes a complex function of canonical variables and time. The corresponding kernel Hamiltonian is derived with $PT$ symmetric canonical-variable transfer in the classical gauge transformation. Moreover, with the change of position-momentum to angle-action variables it is revealed that the non-adiabatic Hannay's angle $Δθ_{H}$ and Berry phase satisfy precisely the quantum-classical correspondence,$γ_{n}=$ $(n+1/2)Δθ_{H}$.

quant-ph↗

arXiv2022

Non-Hermitian Hamiltonian beyond PT-symmetry for time-dependant SU(1,1) and SU(2) systems -- exact solution and geometric phase in pseudo-invariant theory

We investigate in this paper time-dependent non-Hermitian Hamiltonians, which consist respectively of SU(1,1) and SU(2) generators. The former Hamiltonian is PT symmetric but the latter one is not. A time-dependent non-unitary operator is proposed to construct the non-Hermitian invariant, which is verified as pseudo-Hermitian with real eigenvalues. The exact solutions are obtained in terms of the eigenstates of the pseudo-Hermitian invariant operator for both the SU(1,1)and SU(2)systems in a unified manner. Then, we derive the LR phase, which can be separated to the dynamic phase and the geometrical phase. The analytical results are exactly in agreement with those of corresponding Hermitian Hamiltonians in the literature.

quant-ph↗

arXiv2022

$PT$-symmetric non-Hermitian Hamiltonian and invariant operator in periodically driven $SU(1,1)$ system

We study in this paper the time evolution of $PT$-symmetric non-Hermitian Hamiltonian consisting of periodically driven $SU(1,1)$ generators. A non-Hermitian invariant operator is adopted to solve the Schrödinger equation, since the time-dependent Hamiltonian is no longer a conserved quantity. We propose a scheme to construct the non-Hermitian invariant with a $PT$-symmetric but non-unitary transformation operator. The eigenstates of invariant and its complex conjugate form a bi-orthogonal basis to formulate the exact solution. We obtain the non-adiabatic Berry phase, which reduces to the adiabatic one in the slow time-variation limit. A non-unitary time-evolution operator is found analytically. As an consequence of the non-unitarity the ket ($|ψ(t)\rangle $) and bra ($\langle ψ(t)|$) states are not normalized each other. While the inner product of two states can be evaluated with the help of a metric operator. It is shown explicitly that the model can be realized by a periodically driven oscillator.

quant-ph↗

arXiv2019

Measuring outcome correlation for spin-s Bell cat-state and geometric phase induced spin parity effect

In terms of quantum probability statistics the Bell inequality (BI) and its violation are extended to spin-$s$ entangled Schrödinger cat-state (called the Bell cat-state) with both parallel and antiparallel spin-polarizations. The BI is never ever violated for the measuring outcome probabilities evaluated over entire two-spin Hilbert space except the spin-$1/2$ entangled states. A universal Bell-type inequality (UBI) denoted by $p_{s}^{lc}\leq0$ is formulated with the local realistic model under the condition that the measuring outcomes are restricted in the subspace of spin coherent states. A spin parity effect is observed that the UBI can be violated only by the Bell cat-states of half-integer but not the integer spins. The violation of UBI is seen to be a direct result of non-trivial Berry phase between the spin coherent states of south- and north-pole gauges for half-integer spin, while the geometric phase is trivial for the integer spins. A maximum violation bound of UBI is found as $p_{s}^{\max}$=1, which is valid for arbitrary half-integer spin-$s$ states.

quant-ph↗

arXiv2018

Extended Bell inequality and maximum violation

The original formula of Bell inequality (BI) in terms of two-spin singlet has to be modified for the entangled-state with parallel spin polarization. Based on classical statistics of the particle-number correlation, we prove in this paper an extended BI, which is valid for two-spin entangled states with both parallel and antiparallel polarizations. The BI and its violation can be formulated in a unified formalism based on the spin coherent-state quantum probability statistics with the state-density operator, which is separated to the local and non-local parts. The local part gives rise to the BI, while the violation is a direct result of the non-local quantum interference between two components of entangled state. The Bell measuring outcome correlation denoted by $P_{B}$ is always less than or at most equal to one for the local realistic model ($P_{B}^{lc}\leq1$) regardless of the specific superposition coefficients of entangled state. Including the non-local quantum interference the maximum violation of BI is found as $P_{B}^{\max}$ $=2$, which, however depends on state parameters and three measuring directions as well. Our result is suitable for entangled photon pairs.

quant-ph↗

arXiv2018

Maximum violation of Wigner inequality for two-spin entangled states with parallel and antiparallel polarizations

The experimental test of Bell's inequality is mainly focused on Clauser-Horne-Shimony-Holt (CHSH) form, which provides a quantitative bound, while little attention has been pained on the violation of Wigner inequality (WI). Based on the spin coherent state quantum probability statistics we in the present paper extend the WI and its violation to arbitrary two-spin entangled states with antiparallel and parallel spin-polarizations. The local part of density operator gives rise to the WI while the violation is a direct result of non-local interference between two components of the entangled states. The Wigner measuring outcome correlation denoted by $W$ is always less than or at most equal to zero for the local realist model ($% W_{lc_{}}\leq 0$) regardless of the specific initial state. On the other hand the violation of\ WI is characterized by any positive value of $W$, which possesses a maximum violation bound $W_{\max }$ $=1/2$. We conclude that the WI is equally convenient for the experimental test of violation by the quantum entanglement.

quant-ph↗

arXiv2017

Efficient spin-current injection in single-molecule magnet junctions

We study theoretically spin transport through a single-molecule magnet (SMM) in the sequential and cotunneling regimes, where the SMM is weakly coupled to one ferromagnetic and one normalmetallic leads. By a master-equation approach, it is found that the spin polarization injected from the ferromagnetic lead is amplified and highly polarized spin-current can be generated, due to the exchange coupling between the transport electron and the anisotropic spin of the SMM. Moreover, the spin-current polarization can be tuned by the gate or bias voltage, and thus an efficient spin injection device based on the SMM is proposed in molecular spintronics.

cond-mat.mes-hall↗

arXiv2017

Entanglement Dynamics for Two Spins in an Optical Cavity---Field Interaction Induced Decoherence and Coherence Revival

We in this paper study quantum correlations for two neutral spin-particles coupled with a single-mode optical cavity through the usual magnetic interaction. Two-spin entangled states for both antiparallel and parallel spin-polarizations are generated under the photon coherent-state assumption. Based on the quantum master equation we derive the time-dependent quantum correlation of Clauser-Horne-Shimony-Holt (CHSH) type explicitly in comparison with the well known entanglement-measure concurrence. In the two-spin singlet state, which is recognized as one eigenstate of the system, the CHSH correlation and concurrence remain in their maximum values invariant with time and independent of the average photon-numbers either. The correlation varies periodically with time in the general entangled-states for the low average photon-numbers. When the photon number increases to a certain value the oscillation becomes random and the correlations are suppressed below the Bell bound indicating the decoherence of the entangled states. In the high photon-number limit the coherence revivals periodically such that the CHSH correlation approaches the upper bound value at particular time points associated with the cavity-field period

quant-ph↗

arXiv2017

Dicke Phase Transition and Collapse of Superradiant Phase in Optomechanical Cavity with Arbitrary Number of Atoms

We in this paper derive the analytical expressions of ground-state energy, average photon-number, and the atomic population by means of the spin-coherent-state variational method for arbitrary number of atoms in an optomechanical cavity. It is found that the existence of mechanical oscil- lator does not affect the phase boundary between the normal and superradiant phases. However, the superradiant phase collapses by the resonant damping of the oscillator when the atom-field coupling increases to a so-called turning point. As a consequence the system undergoes at this point an additional phase transition from the superradiant phase to a new normal phase of the atomic population-inversion state. The region of superradiant phase decreases with the increase of photon-phonon coupling. It shrinks to zero at a critical value of the coupling and a direct atomic population transfer appears between two atom-levels. Moreover we find an unstable nonzero-photon state, which is the counterpart of the superradiant state. In the absence of oscillator our result re- duces exactly to that of Dicke model. Particularly the ground-state energy for N = 1 (i.e. the Rabi model) is in perfect agreement with the numerical diagonalization in a wide region of coupling constant for both red and blue detuning. The Dicke phase transition remains for the Rabi model in agreement with the recent observation.

quant-ph↗

arXiv2017

Spin-parity effect in violation of bell's inequalities for entangled states of parallel polarization

Bell inequalities (BIs) derived in terms of quantum probability statistics are extended to general bipartite-entangled states of arbitrary spins with parallel polarization. The original formula of Bell for the two-spin singlet is slightly modified in the parallel configuration, while, the inequality for- mulated by Clauser-Horne-Shimony-Holt remains not changed. The violation of BIs indeed resulted from the quantum non-local correlation for spin-1=2 case. However, the inequalities are always satisfied for the spin-1 entangled states regardless of parallel or antiparallel polarizations of two spins. The spin parity effect originally demonstrated with the antiparallel spin-polarizations (Mod. Phys. Lett. B28, 145004) still exists for the parallel case. The quantum non-locality does not lead to the violation for integer spins due to the cancellation of non-local interference effects by the quantum statistical-average. Again the violation of BIs seems a result of the measurement induced nontrivial Berry-phase for half-integer spins.

quant-ph↗

arXiv2015

Photon Devil's staircase: photon long-range repulsive interaction in lattices of coupled resonators with Rydberg atoms

The realization of strong coherent interactions between individual photons is a long-standing goal in science and engineering. In this report, based on recent experimental setups, we derive a strong photon long-range repulsive interaction, by controlling the van der Waals repulsive force between Cesium Rydberg atoms located inside different cavities in extended Jaynes-Cummings-Hubbard Lattices. We also find novel quantum phases induced by this photon long-range repulsive interaction. For example, without photon hopping, a photon Devil's staircase, induced by the breaking of long-range translation symmetry, can emerge. If photon hopping occurs, we predict a photon-floating solid phase, due to the motion of particle-and hole-like defects. More importantly, for a large chemical potential in the resonant case, the photon hopping can be frozen even if the hopping term exists. We call this new phase the photon-frozen solid phase. In experiments, these predicted phases could be detedted by measuring the number of polaritons via resonance fluorescence.

quant-ph↗

arXiv2014

Quantum phases in circuit QED with a superconducting qubit array

Circuit QED on a chip has become a powerful platform for simulating complex many-body physics. In this report, we realize a Dicke-Ising model with an antiferromagnetic nearest-neighbor spin-spin interaction in circuit QED with a superconducting qubit array. We show that this system exhibits a competition between the collective spin-photon interaction and the antiferromagnetic nearest-neighbor spin-spin interaction, and then predict four quantum phases, including: a paramagnetic normal phase, an antiferromagnetic normal phase, a paramagnetic superradiant phase, and an antiferromagnetic superradiant phase. The antiferromagnetic normal phase and the antiferromagnetic superradiant phase are new phases in many-body quantum optics. In the antiferromagnetic superradiant phase, both the antiferromagnetic and superradiant orders can coexist, and thus the system possesses $Z_{2}^{z}\otimes Z_{2}$\ symmetry. Moreover, we find an unconventional photon signature in this phase. In future experiments, these predicted quantum phases could be distinguished by detecting both the mean-photon number and the magnetization.

quant-ph↗

arXiv2013

Intrinsic spin-relaxation induced negative tunnel magnetoresistance in a single-molecule magnet

We investigate theoretically the effects of intrinsic spin-relaxation on the spin-dependent transport through a single-molecule magnet (SMM), which is weakly coupled to ferromagnetic leads. The tunnel magnetoresistance (TMR) is obtained by means of the rate-equation approach including not only the sequential but also the cotunneling processes. It is shown that the TMR is strongly suppressed by the fast spin-relaxation in the sequential region and can vary from a large positive to slight negative value in the cotunneling region. Moreover, with an external magnetic field along the easy-axis of SMM, a large negative TMR is found when the relaxation strength increases. Finally, in the high bias voltage limit the TMR for the negative bias is slightly larger than its characteristic value of the sequential region, however it can become negative for the positive bias caused by the fast spin-relaxation.

cond-mat.mes-hall↗

arXiv2013

Quantum Non-localities and Correlation-Measurement-Induced Berry Phases for Spin-Singlet States

We in this Letter derive analytic formulas of Bell correlations in terms of quantum probability statistics under the assumption of measuring outcome-independence. For a spin-1/2 singlet state we find analytically that the violations of Bell-type inequalities are really related to the quantum non-local correlations. However, the Bell and Clauser-Horne-Shimony-Holt (CHSH) inequalities are always satisfied for the spin-1 singlet states. More generally the quantum non-locality does not lead to the violation of Bell and CHSH inequalities for the integer-spin singlet since the non-local interference effects cancel each other by the quantum statistical-average. Such a cancellation no longer exists for the half-integer spin singlets due to the nontrivial Berry phase, and thus the relevant Bell-type inequalities can be violated. Specifically, our generic observations can be experimentally tested with the entangled photon-pairs. Our arguments are based on the spin-singlet states, but could be generalized to other bipartite quantum states.

quant-ph↗

arXiv2012

Thermodynamics of spin-orbit-coupled Bose-Einstein condensates

In this paper we develop a quantum field approach to reveal the thermodynamic properties of the trapped BEC with the equal Rashba and Dresselhaus spin-orbit couplings. In the experimentally-feasible regime, the phase transition from the separate phase to the single minimum phase can be well driven by the tunable temperature. Moreover, the critical temperature, which is independent of the trapped potential, can be derived exactly. At the critical point, the specific heat has a large jump and can be thus regarded as a promising candidate to detect this temperature-driven phase transition. In addition, we obtain the analytical expressions for the specific heat and the entropy in the different phases. In the single minimum phase, the specific heat as well as the entropy are governed only by the Rabi frequency. However, in the separate phase with lower temperature, we find that they are determined only by the strength of spin-orbit coupling. Finally, the effect of the effective atom interaction is also addressed. In the separate phase, this effective atom interaction affects dramatically on the critical temperature and the corresponding thermodynamic properties.

cond-mat.quant-gas↗