arXiv subjects

Zhiguo Lü

Publications and source records attributed to Zhiguo Lü.

At least 19 recordsLinked to original sources

arXiv2024

Variational approach to light-matter interaction: Bridging quantum and semiclassical limits

We present a time-dependent variational approach with the multiple Davydov $D_2$ trial state to simulate the dynamics of light-matter systems when the field is in a coherent state with an arbitrary finite mean photon number. The variational approach captures not only the system dynamics but also the field dynamics and is applicable to a variety of quantum models of light-matter interaction such as the Jaynes-Cummings model, Rabi model, and Dicke model, and is feasible to tackle the multimode quantized fields. By comparison of the variational and semiclassical dynamics of both the system and field, we illustrate that the variational dynamics from the quantum models agrees with those from the corresponding semiclassical models as long as the mean number of photons is sufficiently large. Moreover, we illustrate that in the crossover between the quantum and semiclassical limits, the quantum corrections lead to the collapse of the oscillations in dynamics, which is absent in the semiclassical models. The variational approach provides a unified treatment of light-matter interaction from the quantum to the semiclassical limit.

quant-ph↗

arXiv2023

Resonance of Geometric Quantities and Hidden Symmetry in the Asymmetric Rabi Model

We present the interesting resonance of two kinds of geometric quantities, namely the Aharonov-Anandan (AA) phase and the time-energy uncertainty, and reveal the relation between resonance and the hidden symmetry in the asymmetric Rabi model by numerical and analytical methods. By combining the counter-rotating hybridized rotating-wave method with time-dependent perturbation theory, we solve systematically the time evolution operator and then obtain the geometric phase of the Rabi model. In comparison with the numerically exact solutions, we find that the analytical results accurately describe the geometric quantities in a wide parameter space. We unveil the effect of the bias on the resonance of geometric quantities, (1) the positions of all harmonic resonances stemming from the shift of the Rabi frequency at the presence of the bias; (2) the occurrence of even order harmonic resonance due to the bias. When the driving frequency is equal to the subharmonics of the bias, the odd higher-order harmonic resonances disappear. Finally, the hidden symmetry has a resemblance to that of the quantum Rabi model with bias, which indicates the quasienergy spectra are similar to the energy spectra of the latter.

quant-ph↗

arXiv2023

Lamb Shift and the Vacuum Rabi Splitting in a Strongly Dissipative Environment

We study the vacuum Rabi splitting of a qubit ultrastrongly coupled to a high-$Q$ cavity mode and a radiation reservoir. Three methods are employed: a numerically exact variational approach with a multiple Davydov ansatz, the rotating-wave approximation (RWA), and the transformed RWA. Agreement between the variational results and the transformed RWA results is found in the regime of validity of the latter, where the RWA breaks down completely. We illustrate that the Lamb shift plays an essential role in modifying the vacuum Rabi splitting in the ultrastrong coupling regime, leading to off-resonant qubit-cavity coupling even though the cavity frequency equals to the bare transition frequency of the qubit. Specifically, the emission spectrum exhibits one broad low-frequency peak and one narrow high-frequency peak in the presence of relatively weak cavity-qubit coupling. As the cavity-qubit coupling increases, the low-frequency peak narrows while the high-frequency peak broadens until they have similar widths.

quant-ph↗

arXiv2023

Multiphoton resonance band and Bloch-Siegert shift in a bichromatically driven qubit

We study the resonance and dynamics of a qubit exposed to a strong aperiodic bichromatic field by using a periodic counter-rotating hybridized rotating wave (CHRW) Hamiltonian, which is derived from the original Hamiltonian with the unitary transformations under a reasonable approximation and enables the application of the Floquet theory. It is found that the consistency between the CHRW results and numerically exact generalized-Floquet-theory (GFT) results in the valid regime of the former while the widely used rotating-wave approximation (RWA) breaks down. We illustrate that the resonance exhibits band structure and the Bloch-Siegert shifts induced by the counter-rotating couplings of the bichromatic field become notable at the multiphoton resonance band. In addition, the CHRW method is found to have a great advantage of efficiency over the GFT approach particularly in the low beat-frequency case where the latter converges very slowly. The present CHRW method provides a highly efficient way to calculate the resonance frequency incorporating the Bloch-Siegert shift and provides insights into the effects of the counter-rotating couplings of the bichromatic field in the strong-driving regimes.

quant-ph↗

arXiv2023

Emission spectral non-Markovianity in qubit-cavity systems in the ultrastrong coupling regime

We study the emission spectra of dissipative Rabi and Jaynes-Cummings models in the non-Markovian and ultrastrong coupling regimes. We have derived a polaron-transformed Nakajima-Zwanzig master equation (PTNZE) to calculate the emission spectra, which eliminates the well known limitations of the Markovian approximation and the standard second-order perturbation. Using the time-dependent variational approach as benchmark, the PTNZE is found to yield accurate emission spectra in certain ultrastrong coupling regimes where the standard second-order Nakajima-Zwanzig master equation breaks down. It is shown that the emission spectra of the dissipative Rabi and Jaynes-Cummings models are in general asymmetric under various initial conditions. Direct comparisons of spectra for the two models illustrate the essential role of the qubit-cavity counter-rotating term and the spectra features under different qubit-cavity coupling strengths and system initial conditions.

quant-ph↗

arXiv2022

Dynamics of the spin-boson model: the effect of bath initial conditions

Dynamics of the (sub-)Ohmic spin-boson model under various bath initial conditions is investigated by employing the Dirac-Frenkel time-dependent variational approach with the multiple Davydov $\mathrm{D_1}$ ansatz in the interaction picture. The validity of our approach is carefully checked by comparing results with those of the hierarchy equations of motion method. By analyzing the features of nonequilibrium dynamics, we identify the phase diagrams for different bath initial conditions. We find that for spectral exponent $s<s_c$, there exists a transition from coherent to quasicoherent dynamics with increasing the coupling strengths. For $s_c<s\leq{1}$, the coherent to incoherent crossover occurs at a certain coupling strength, and the quasicoherent dynamics emerges at much larger couplings. The initial preparation of the bath has considerable influence on the dynamics.

physics.chem-ph↗

arXiv2022

Engineered Tunable Decay Rate and Controllable Dissipative Dynamics

We investigate the steering dissipative dynamics of a two-level system (qubit) by means of the modulation of an assisted tunneling degree of freedom which is described by a quantum-oscillator spin-boson model. Our results reveal that the decoherence rate of the qubit can be significantly suppressed and simultaneously its quality factor is enhanced. Moreover, the modulated dynamical susceptibility exhibits a multi-peak feature which is indicative of the underlying structure and measurable in experiment. Our findings demonstrate that the interplay between the combined degrees of freedom and the qubit is crucial for reducing the dissipation of qubit and expanding the coherent regime of quantum operation much large. The strategy might be used to fight against deterioration of quantum coherence in quantum information processing.

quant-ph↗

arXiv2021

Geometric phase and non-adiabatic resonance of the Rabi model

We investigate the effects of counterrotating terms on geometric phase and its relation to the resonance of the Rabi model. We apply the unitary transformation with a single parameter to the Rabi model and obtain the transformed Hamiltonian involving multiple harmonic terms. By combining the counter-rotating-hybridized rotating-wave method with time-dependent perturbation theory, we solve systematically time evolution operator and then obtain the geometric phase of the two-level system. Our results are beyond adiabatic approximation and rotating-wave approximation (RWA). Higher-order harmonic resonance happens when driving frequency is equal to higher-order subharmonic of the Rabi frequency. In comparison with numerically exact results, our calculated results are accurate over a wide range of parameters space, especially in higher-order harmonic resonance regimes. In these regimes we demonstrate geometric phases change dramatically while those of the RWA are smooth. The RWA is thoroughly invalid even if the driving strength is extremely weak. We find it is the higher-order harmonic terms that play an important role on the cyclic state and demonstrate the characters of geometric phase in higher-order harmonic resonance regime. We also present analytical formalism of the change rate of geometric phase and quasienergies, which agree well with numerically exact ones even in the strong driving case. The developed method can be applied to explore the dynamics of strongly driven qubits and physical properties of higher-order harmonic processes.

quant-ph↗

arXiv2020

Plateau dynamics with quantized oscillations of a strongly driven qubit

We present an interesting dynamical temporal localization of a strongly driven two-level system (TLS), a plateau with quantized oscillation, by an analytical and transparent method, the counter-rotating-hybridized rotating-wave (CHRW) method. This approach, which is based on unitary transformations with a single parameter, treats the rotating and counter-rotating terms on equal footing. In the unitarily transformed representation, we find that it is the multiple-harmonic terms shown in the transformed Hamiltonian that make a crucial contribution to the generation of the exotic plateau phenomenon. By comparing the results of the numerically exact calculation and several other methods, we show that the CHRW results obtained by analytical formalism involving the collective effects of multiple harmonics are in good agreement with the numerical results, which illustrates not only the general tendency of the dynamical evolution of strongly driven TLS, but also the interesting phenomena of plateaus. The developed CHRW method reveals two kinds of plateau patterns: zigzag plateau and armchair plateau. The plateau phenomenon has a periodical pattern whose frequency is double the driving frequency, and possesses quantized oscillations the number of which has a certain, precise value. Besides, fast oscillation is produced on every plateau which is determined by the relevant driving parameters of the TLS. Our main results are as follows: (i) in the large-amplitude oscillatory case, it turns out that the collective effects of all even harmonics contribute to the generation of zigzag plateau with quantized oscillation; (ii) in the small-amplitude oscillatory case, the dynamics of the coherent destruction of tunneling under strong driving is exactly exhibited by including the odd-harmonic effect, namely, armchair plateau possessing a two-stair structure rather than the complete destruction.

quant-ph↗

arXiv2020

Role of generalized parity in the symmetry of fluorescence spectrum from two-level systems under periodic frequency modulation

We study the origin of the symmetry of the fluorescence spectrum from the two-level system subjected to a low-frequency periodic modulation and a near-resonant high-frequency monochromatic excitation by using the analytical and numerical methods based on the Floquet theory. We find that the fundamental origin of symmetry of the spectrum can be attributed to the presence of the generalized parity of the Floquet states, which depends on the driving parameters. The absence of the generalized parity can lead to the asymmetry of the spectrum. Based on the generalized parity, the conditions for the symmetry and asymmetry of the spectrum can be derived, which succeeds in predicting symmetry and asymmetry of the spectrum for the harmonic, biharmonic, and multiharmonic modulations. Moreover, we find that the secular approximation widely used in the analytical calculation may lead to artifact symmetry of the spectrum that vanishes when such approximation is avoided. The present study provides a significant perspective on the origin of the symmetry of the spectrum.

quant-ph↗

arXiv2018

Effects of counterrotating interaction on driven tunneling dynamics: coherent destruction of tunneling and Bloch-Siegert shift

We investigate the dynamics of a driven two-level system (classical Rabi model) using the counter-rotating-hybridized rotating wave method (CHRW), which is a simple method based on a unitary transformation with a parameter $ξ$. This approach is beyond the traditional rotating-wave approximation (Rabi-RWA) and more importantly, remains the RWA form with a renormalized tunneling strength and a modified driving strength. The reformulated rotating wave method not only possesses the same mathematical simplicity as the Rabi-RWA but also allows us to explore the effects of counter-rotating (CR) components. We focus on the properties of off-resonance cases for which the Rabi-RWA method breaks down. After comparing the results of different RWA schemes and those of the numerically exact method in a wide range of parameter regime, we show that the CHRW method gives the accurate driven dynamics which is in good agreement with the numerical method. Moreover, the other RWA methods appear as various limiting cases of the CHRW method. The CHRW method reveals the effects of the CR terms clearly by means of coherent destruction of tunneling and Bloch-Siegert shift. Our main results are as follows: (i) the dynamics of the coherent destruction of tunneling is explicitly given and its dependence on $Δ$ is clarified, which is quantitatively in good agreement with the exact results; (ii) the CR modulated Rabi frequency and the Bloch-Siegert shift are analytically calculated, which is the same as the exact results up to fourth order; (iii) the validity of parameter regions of different RWA methods are given and the comparison of dynamics of these methods are shown. Since the CHRW approach is mathematically simple as well as tractable and physically clear, it may be extended to some complicated problems where it is difficult to do a numerical study.

cond-mat.mes-hall↗

arXiv2017

Protecting coherence by reservoir engineering: intense bath disturbance

We put forward a scheme based on reservoir engineering to protect quantum coherence from leaking to bath, in which we intensely disturb the Lorentzian bath by N harmonic oscillators. We show that the intense disturbance changes the spectrum of the bath and reduces the qubit-bath interaction. Furthermore, we give the exact time evolution with the Lorentzian spectrum by a master equation, and calculate the concurrence and survival probability of the qubits to demonstrate the effect of the intense bath disturbance on the protection of coherence. Meanwhile, we reveal the dynamic effects of counter-rotating interaction on the qubits as compared to the results of the rotating wave approximation.

quant-ph↗

arXiv2017

Quantum Zeno and anti-Zeno effects in open quantum systems

Traditional approach on quantum Zeno effect (QZE) and quantum anti-Zeno effect (QAZE) in open quantum systems (implicitly) assumes the bath (environment) state returning to its original state after each instantaneous projective measurement on the system and thus ignores the cross-correlations of the bath operators between different Zeno intervals. However, this assumption is not generally true, especially for a bath with a considerably non-negligible memory effect and for a system repeatedly projected into an initial general superposition state. We find that in stark contrast to the result of a constant value found in the traditional approach, the scaled average decay rate in unit Zeno interval of the survival probability is generally time-dependent or has an oscillatory behavior. In the case of strong bath correlation, the transition between the QZE and QAZE depends sensitively on the number of measurements $N$. For a fixed $N$, a QZE region predicted by the tradition approach may be in fact already in the QAZE region. We illustrate our findings using an exactly solvable open qubit system model with a Lorentzian bath spectral density, which is directly related to realistic circuit cavity quantum electrodynamics systems. Thus the results and dynamics presented here can be verified by current superconducting circuit technology.

quant-ph↗

arXiv2017

Topology-Induced Symmetry Breaking for Vortex with Artificial Monopole

We construct an artificial U(1) gauge field in the cold atom system to form a monopole along with vortices. It is supposed that the cold atoms are confined on a spherical surface, and two sets of identical laser beams in the opposite propagating directions shine on two sides of the sphere. Arbitrary Chern number CN, proportional to the quantized magnetic flux, can be obtained by selecting proper laser modes. This construction meets the condition of Chern's theorem, so that the vortices of the atom wave function will emerge on the sphere, whose winding number equals CN. It is found that a geometric symmetry is broken spontaneously for odd CN, which corresponds to a topology-induced quantum phase transition. In particular for CN=1, the ground state of the cold atoms are double-degenerate and can be applied to make a stable qubit. Since the ground-state degeneracy is protected by topology-induced symmetry breaking against dissipation, the proposed topological structure has vast potential in quantum storage.

quant-ph↗

arXiv2016

Bias-modulated dynamics of a strongly driven two-level system

We investigate the bias-modulated dynamics of a strongly driven two-level system using the counter-rotating-hybridized rotating-wave (CHRW) method. This CHRW method treats the driving field and the bias on equal footing by a unitary transformation with two parameters $ξ$ and $ζ$, and is nonperturbative in driving strength, tunneling amplitude or bias. In addition, this CHRW method is beyond the traditional rotating-wave approximation (Rabi-RWA) and yet by properly choosing the two parameters $ξ$ and $ζ$, the transformed Hamiltonian takes the RWA form with a renormalized energy splitting and a renormalized driving strength. The reformulated CHRW method possesses the same mathematical simplicity as the Rabi-RWA approach and thus allows us to calculate analytically the dynamics and explore explicitly the effect of the bias. We show that the CHRW method gives the accurate driven dynamics for a wide range of parameters as compared to the numerically exact results. When energy scales of the driving are comparable to the intrinsic energy scale of the two-level systems, the counter-rotating interactions and static bias profoundly influence the generalized Rabi frequency. In this regime, where ordinary perturbation approaches fail, the CHRW works very well and efficiently. We also demonstrate the dynamics of the system in the strong-driving and off-resonance cases for which the Rabi-RWA method breaks down but the CHRW method remains valid. We obtain analytical expressions for the generalized Rabi frequency and bias-modulated Bloch-Siegert shift as functions of the bias, tunneling and driving field parameters. The CHRW approach is a mathematically simple and physically clear method. It can be applied to treat some complicated problems for which a numerical study is difficult to perform.

quant-ph↗

arXiv2016

Resonance fluorescence of strongly driven two-level system coupled to multiple dissipative baths

We present a theoretical formalism for resonance fluorescence radiating from a two-level system (TLS) driven by any periodic driving and coupled to multiple reservoirs. The formalism is derived analytically based on the combination of Floquet theory and Born-Markov master equation. The formalism allows us to calculate the spectrum when the Floquet states and quasienergies are analytically or numerically solved for simple or complicated driving fields. We can systematically explore the spectral features by implementing the present formalism. To exemplify this theory, we apply the unified formalism to comprehensively study a generic model that a harmonically driven TLS is simultaneously coupled to a radiative reservoir and a dephasing reservoir. We demonstrate that the significant features of the fluorescence spectra, the driving-induced asymmetry and the dephasing-induced asymmetry, can be attributed to the violation of detailed balance condition, and explained in terms of the driving-related transition quantities between Floquet-states and their steady populations. In addition, we find the distinguished features of the fluorescence spectra under the biharmonic and multiharmonic driving fields in contrast with that of the harmonic driving case. In the case of the biharmonic driving, we find that the spectra is significantly different from the result of the rotating-wave approximation (RWA) under the multiple resonance conditions. By the three concrete applications, we illustrate that the present formalism provides a routine tool for comprehensively exploring the fluorescence spectrum of periodically strongly driven TLSs.

quant-ph↗

arXiv2015

Bloch-Siegert shift of the Rabi model

We apply a simple analytical method based on a unitary transformation to calculate the Bloch-Siegert (BS) shift over the entire driving-strength range. In quantitative comparison with the numerically exact BS shift obtained by Floquet formalism as well as the previous BS results, we confirm that our calculated results are not only accurate in the weak-driving regime but also correct in strong-driving limit. In the intermediate strong-driving regime, the calculated values of the BS shift are nearly the same as the exact ones. It turns out that our calculation for the BS shift is beyond perturbation. Meanwhile, we demonstrate the signatures caused by the BS shift by monitoring the excited-state population and the probe-pump spectrum under the experiment accessible conditions. In particular, we find that when the driving frequency is fixed at the transition frequency of the system, the lineshape of the probe-pump spectrum becomes asymmetric with the increase of the driving strength, which may be verified experimentally.

quant-ph↗

arXiv2015

An ansatz to the quantum phase transition in a dissipative two-qubit system

By means of a unitary transformation, we propose an ansatz to study quantum phase transitions in the ground state of a two-qubit system interacting with a dissipative reservoir. First, the ground state phase diagram is analyzed in the presence of the Ohmic and sub-Ohmic bath using an analytic ground state wave function which takes into account the competition between intrasite tunneling and intersite correlation. The quantum critical point is determined as the transition point from non-degenerate to degenerate ground state and our calculated critical coupling strength $α_c$ agrees with that from the numerical renormalization group method. Moreover, by computing the entanglement entropy between the qubits and the bath as well as the qubit-qubit correlation function in the ground state, we explore the nature of the quantum phase transition between the delocalized and localized states.

quant-ph↗