Quantum phase transitions in the sub-Ohmic spin-boson model: failure of the quantum-classical mapping

The effective theories for many quantum phase transitions can be mapped onto those of classical transitions. Here we show that the naive mapping fails for the sub-Ohmic spin-boson model which describes a two-level system coupled to a bosonic bath with power-law spectral density, J(omega) proportional, variantomega(s). Using an epsilon expansion we prove that this model has a quantum transition controlled by an interacting fixed point at small s, and support this by numerical calculations. In contrast, the corresponding classical long-range Ising model is known to display mean-field transition behavior for 0 < s < 1/2, controlled by a noninteracting fixed point. The failure of the quantum-classical mapping is argued to arise from the long-ranged interaction in imaginary time in the quantum model.     

Calculation of the thermal conductivity and the specific heat of the lattice for a spin-boson system at low temperatures

The thermal conductivity of the lattice is calculated for a spin-boson system using the method of inverse linear response theory. The spin-boson Hamiltonian consists of coupled two-level systems (TLS) represented by pseudospin operators, acoustical phonons and an interaction between both systems. The lattice specific heat is determined in the framework of perturbation theory with respect to spin-boson coupling. For the calculation of both quantities results for spin-correlation functions derived within self-consistent random phase approximation are applied. At low temperatures the influence of spin-boson coupling and of interacting TLS on the temperature dependence of the lattice thermal conductivity and of the lattice specific heat is discussed and compared with corresponding experimental investigations.     

Entanglement of a two-level atom and its spontaneous emission near the edge of a photonic band gap

The entanglement of a two-level atom and its radiation field near the edge of a photonic band gap is studied by using the quantum entropy. Unlike the free space case, there is a steady-state entanglement between the atom and its spontaneous emission field even when the atomic transition frequency lies outside the band gap. Moreover, the degree of entanglement, which is due to the formation of atom–photon bound dressed state, depends on the detuning of the atomic transition frequency from the photonic band edge and can be controlled by a controllable photonic band gap crystal.     

Entanglement entropy, decoherence, and quantum phase transitions of a dissipative two-level system

The concept of entanglement entropy appears in multiple contexts, from black hole physics to quantum information theory, where it measures the entanglement of quantum states. We investigate the entanglement entropy in a simple model, the spin-boson model, which describes a qubit (two-level system) interacting with a collection of harmonic oscillators that models the environment responsible for decoherence and dissipation. The entanglement entropy allows to make a precise unification between entanglement of the spin with its environment, decoherence, and quantum phase transitions. We derive exact analytical results which are confirmed by Numerical Renormalization Group arguments both for an ohmic and a subohmic bosonic bath. The entanglement entropy obeys universal scalings. We make comparisons with entanglement properties in the quantum Ising model and in the Dicke model. We also emphasize the possibility of measuring this entropy using charge qubits subject to electromagnetic noise; such measurements would provide an empirical proof of the existence of entanglement entropy.     

Decoherence of spin-deformed bosonic model

The decoherence rate and some parameters affecting it are investigated for the generalized spin-boson model. We consider the spin-bosonic model when the bosonic environment is modeled by the deformed harmonic oscillators. We show that the state of the environment approaches a non-linear coherent state. Then, we obtain the decoherence rate of a two-level system which is in contact with a deformed bosonic environment which is either in thermal equilibrium or in the ground state. By using some recent realization of f$f$-deformed oscillators, we show that some physical parameters strongly affect the decoherence rate of a two-level system.     

Controllable Absorption and Dispersion Properties of an RF-drivenFive-Level Atom in a Double-Band Photonic-Band-Gap Material

The probe absorption-dispersion spectra of a radio-frequency (RF)-driven five-level atom embedded in a photonic crystal are investigated by considering the isotropic double-band photonic-band-gap (PBG) reservoir. In the model used, the two transitions are, respectively, coupled by the upper and lower bandsin such a PBG material, thus leading to some curious phenomena. Numerical simulations are performed for the optical spectra. It is found that when one transition frequency is inside the band gap and the other is outside the gap, there emerge three peaks in the absorption spectra. However, for the case that two transition frequencies lie inside or outside the band gap, the spectra display four absorption profiles. Especially, there appear two sharp peaksin the spectra when both transition frequencies exist inside the band gap. The influences of the intensity and frequency of the RF-driven field on the absorptive and dispersive response are analyzed under different band-edge positions. It is found that a transparency window appears in the absorption spectra and is accompanied by a very steep variation of the dispersion profile by adjusting system parameters. These results show that the absorption-dispersion properties of the system depend strongly on the RF-induced quantum interference and the density of states (DOS) of the PBG reservoir.     

Multiphoton transitions in a macroscopic quantum two-state system

We have observed multiphoton transitions between two macroscopic quantum-mechanical superposition states formed by two opposite circulating currents in a superconducting loop with three Josephson junctions. Resonant peaks and dips of up to three-photon transitions were observed in spectroscopic measurements when the system was irradiated with a strong rf-photon field. The widths of the multiphoton absorption dips are shown to scale with the Bessel functions in agreement with theoretical predictions derived from the Bloch equation or from a spin-boson model.     

The influence of the dipole-dipole interaction and atomic coherence on the entanglement of two atoms with degenerate two-photon transitions

Entanglement of two artificial two-level atoms with degenerate two-photon transitions is considered in the case in which the atoms interact with the thermal single-mode field in an ideal cavity. The possibility of controlling the atomic entanglement degree in such a system due to the induction of atomic coherence and direct dipole-dipole interaction of atoms is shown.     

The equilibrium states of the spin-boson model

The temperature states of the spin-boson model consisting of a two-level atom in a Bose field are studied. It is proved that for all temperatures there exists a unique solution, hence there is no spontaneous reflection symmetry breaking.Bevoegdverklaard Navorser N.F.W.O. BelgiumOnderzoeker I.I.K.W. Belgium     

Atom-molecule Rabi oscillations in a Mott insulator

We observe large-amplitude Rabi oscillations between an atomic and a molecular state near a Feshbach resonance. The experiment uses 87Rb in an optical lattice and a Feshbach resonance near 414 G. The frequency and amplitude of the oscillations depend on the magnetic field in a way that is well described by a two-level model. The observed density dependence of the oscillation frequency agrees with theoretical expectations. We confirmed that the state produced after a half-cycle contains exactly one molecule at each lattice site. In addition, we show that, for energies in a gap of the lattice band structure, the molecules cannot dissociate.     

The Peierls system in a light field

This paper studies the behavior of the low-temperature phase of the Peierls system in a quasimonochromatic time-independent random light field whose frequency is much lower than the frequency of the lower edge of band-to-band transitions. The density matrix method in the dipole approximation is used to derive equations for the band gap. A dependence between the band gap and the light-field intensity is established in an approximation in which the concentration of the nonequilibrium electrons in the conduction band is low. The possibility of, and the conditions for, the existence of a light-induced semiconductor-semiconductor phase transition and cavityless optical bistability with increasing absorption are established. Zh. éksp. Teor. Fiz. 111, 1398–1409 (April 1997)     

Equilibrium and nonequilibrium dynamics of the sub-Ohmic spin-boson model

Employing the nonperturbative numerical renormalization group method, we study the dynamics of the spin-boson model, which describes a two-level system coupled to a bosonic bath with a spectral density J(omega) proportional to omega(s). We show that, in contrast with the case of Ohmic damping, the delocalized phase of the sub-Ohmic model cannot be characterized by a single energy scale only, due to the presence of a nontrivial quantum phase transition. In the strongly sub-Ohmic regime, s<1, weakly damped coherent oscillations on short time scales are possible even in the localized phase--this is of crucial relevance, e.g., for qubits subject to electromagnetic noise.     

The atom-photon entanglement of a two-level system embedded in double-band photonic band edge

The entanglement of a two-level atom with its spontaneously emitted photon embedded in double-band anisotropic photonic crystal has been investigated via the method of the quantum entropy. Different from the case in an isotropic crystal or in vacuum, the entanglement has symmetrical properties and much slower entanglement rate near the two band edges. Moreover, as a result of the atom-photon bound states by the virtue of the localization around the emitting atom, the degree of the entanglement gradually increases, achieves the maximum and then sharply reduces to zero on the boundary of forbidden band gap as the atomic frequency moves from the center of the band gap to either of the band edges.     

本征GaAs中电子自旋极化的能量演化研究

采用时间分辨圆偏振光抽运-探测光谱,研究9.6 K温度下本征GaAs中电子自旋相干弛豫动力学,发现反映电子自旋相干的吸收量子拍的振幅随光子能量的增加呈非单调性变化.考虑自旋极化依赖的带填充效应和带隙重整化效应,发展了圆偏振光抽运-探测光谱的理论模型.该模型表明量子拍的振幅依赖于所探测能级的电子初始自旋极化度,自旋探测灵敏度以及带填充因子,三者的乘积导致了量子拍振幅的非单调变化,与实验结果一致.给出了能级分裂的二能级系统中电子自旋极化度定义.发现在高能级上可以获得100%的初始电子自旋极化度. 关键词： 圆偏振光抽运-探测光谱 吸收量子拍 电子自旋极化度 GaAs     

类Kerr介质中两能级原子与驱动场作用时的相干性

两能级原子被嵌制在一充满类Kerr介质的热库中,通过求解原子与外加驱动场相互作用时约化密度算符非对角元,研究简并双光子过程中原子在外界环境(类Kerr介质和热库)下的相干特性.结果表明:当原子的相干性被保持时,外加驱动场的时间演化与原子的跃迁频率、原子偶极矩和模平均光子数等因素有关.     

内禀退相干下薛定谔猫态光场与原子相互作用系统的场熵演化

通过求解系统的Milburn方程,研究了二能级原子与薛定谔猫态光场相互作用系统中的场熵演化特性.讨论了内禀退相干,光场强度,相干态间的相位角对场熵演化的影响.结果表明: 内禀退相干下,随着时间的演化,场熵振荡逐渐减弱,光场与原子的纠缠度逐渐趋于恒值.并且光场与原子的最大纠缠度值只取决光场强度和相干态间的相位角,与内禀退相干因子无关.光场强度较小时,奇相干态光场与原子的纠缠度最大;偶相干态光场与原子的纠缠度值为最小;Yurke-Stoler相干态光场与原子的纠缠度值介于两者之间. 当内禀退相干因子不变、光场强度较大时,分别处于Yurke-Stoler相干态、偶相干态和奇相干态的光场与原子的纠缠度值趋近于相同.     

内禀退相干下薛定谔猫态光场与原子相互作用系统的场熵演化

通过求解系统的Milburn方程,研究了二能级原子与薛定谔猫态光场相互作用系统中的场熵演化特性.讨论了内禀退相干,光场强度,相干态间的相位角对场熵演化的影响.结果表明: 内禀退相干下,随着时间的演化,场熵振荡逐渐减弱,光场与原子的纠缠度逐渐趋于恒值.并且光场与原子的最大纠缠度值只取决光场强度和相干态间的相位角,与内禀退相干因子无关.光场强度较小时,奇相干态光场与原子的纠缠度最大;偶相干态光场与原子的纠缠度值为最小;Yurke-Stoler相干态光场与原子的纠缠度值介于两者之间. 当内禀退相干因子不变、光场强度较大时,分别处于Yurke-Stoler相干态、偶相干态和奇相干态的光场与原子的纠缠度值趋近于相同.     

Numerical renormalization group for bosonic systems and application to the sub-ohmic spin-boson model

We describe the generalization of Wilson's numerical renormalization group method to quantum impurity models with a bosonic bath, providing a general nonperturbative approach to bosonic impurity models which can access exponentially small energies and temperatures. As an application, we consider the spin-boson model, describing a two-level system coupled to a bosonic bath with power-law spectral density, J(omega) proportional to omega(s). We find clear evidence for a line of continuous quantum phase transitions for sub-Ohmic bath exponents 0相似文献   

Mode-coupling theory for the dynamics of tunnelling systems in dielectrics

A mode-coupling theory (MCT) is presented for the spin-boson model with a spectral density which accounts for a heat bath made up of lattice vibrations of a dielectric solid (superohmic dissipation). A usual decoupling approximation provides a set of non-linear integral equations which are solved both numerically by iteration on a computer and analytically by means of a frequency dependent ansatz for the memory functions. There is a transition to incoherent motion at a temperatureT ^* where the bare two-level energy is equal to the damping rate, in contradiction to results obtained previously from a path integral formulation. The discrepancy arises since in the MCT the relevant self-energy function does not exhibit a 1/z-pole atz=0. For tunnelling systems in dielectrics this yields a new relaxation mechanism due to incoherent tunnelling: the present results might require to modify some of the basic assumptions of the standard tunnelling model for dielectric glasses.     

Dynamics of a dissipative two level system

We consider the tunneling of a particle in a symmetric double well, which is coupled to its environment in a way, that classically corresponds to a damping constant γ. In the two lowest level subspace, this is described by a spin-boson model with a finite density of zero energy excitations. A relaxation kernel method is applied to calculate the low temperature, low frequency static and dynamical susceptibility. In particular we determine the average tunneling frequency, which is equivalent to the rate for the destruction of phase coherence. For weak damping this is shown to be finite in the limitT→0, whereas for large γ it vanishes with a power low inT. AtT=0 the two regimes are separated by a phase boundary, dividing regions with finite or zero effective tunnel splitting. We discuss the application of the model to the dynamics of flux states in SQUID's and also to paraelectric impurities.