Alternative method for exact diagonalization of the Hamiltonian describing a two-level system coupled to a bose gas with an Einstein spectrum

A simple method is described which exactly diagonalizes the Hamiltonian describing a two-level system coupled to a Bose gas with an Einstein spectrum. The method is based on a separation of the boson field into two mutually orthogonal (and commuting) parts, one of which corresponds to the bound spectrum, the other corresponds to the continuous spectrum. It is also shown that such an additive, linear, field-splitting method is inadequate for the case of a nonconstant spectrum.     

Relaxation of a single two-level system

A relaxation problem for a single two-level system coupled to a Bose field is investigated. The stationary state and relaxation time of the system is analysed. The correction to the unperturbed stationary state is derived in the fourth order of the interaction between the system and bosons. The criteria for an application of the perturbation calculation are discussed.Supported in part by the Polish Academy of Sciences under Contract No. MR I-9.The author would like to express his sincere thanks to the members of the Department of Theoretical Physics at the Silesian University for their comments and discussions.     

Relaxation of the ideal Bose gas

For the ideal Bose gas we study the approach to equilibrium. Above the critical temperature we prove exponential behaviour, with a relaxation time of the order (T-T _c)^-2 around T _c. For T _c we find the t ^-1 law for the two-point function.     

The dynamics of three coupled dipolar Bose Einstein condensates

The dynamics of the three coupled dipolar Bose–Einstein condensates containing N bosons is investigated within a mean-field semiclassical picture based on the coherent-state method. Varieties of periodic solutions （configured as vortex, single depleted well, and dimerlike states） are obtained analytically when the fixed points are identified on the N=constant. The system dynamics are studied via numeric integration of trimer motion equations, thus revealing macroscopic effects of population inversion and self-trapping with different initial states. In particular, the trajectory of the oscillations of the populations in each well shows how the dynamics of the condensates are effected by the presence of dipole–dipole interaction and gauge field.     

Spin orbit coupled Bose Einstein condensate in a two dimensional bichromatic optical lattice

We numerically investigate the localization of Bose Einstein condensate (BEC) with spin orbit coupling in a two dimensional bichromatic optical lattice. We study localization in weakly interacting and non-interacting regimes. The existence of stationary localized states in the presence of spin–orbit and Rabi couplings has been confirmed. We find that spin orbit coupling favors localization, whereas Rabi coupling has a slight delocalization effect.     

Decoherence in a two-level system coupled to a fermion environment with phase transitions

The decoherence process characterized by Loschmidt echo (LE) in a two-level system dephasingly coupled to a fermion environment with phase transitions is studied in this Letter. The results show that the LE of the two-level system may act as a witness of the environment's phase transitions, which is similar to the relation between quantum phase transitions and the LE.     

Optomechanically induced transparency with Bose Einstein condensate in double-cavity optomechanical system

We propose a novel technique of generating multiple optomechanically induced transparency(OMIT) of a weak probe field in hybrid optomechanical system. This system consists of a cigar-shaped Bose–Einstein condensate(BEC), trapped inside each high finesse Fabry-Pérot cavity. In the resolved sideband regime, the analytic solutions of the absorption and the dispersion spectrum are given. The tunneling strength of the two resonators and the coupling parameters of the each BEC in combination with the cavity field have the appearance of three distinct OMIT windows in the absorption spectrum.Furthermore, whether there is BEC in each cavity is a key factor in the number of OMIT windows determination. The technique presented may have potential applications in quantum engineering and quantum information networks.     

Production of a chromium Bose–Einstein condensate

The recent achievement of Bose–Einstein condensation of chromium atoms [1] has opened longed-for experimental access to a degenerate quantum gas with long-range and anisotropic interaction. Due to the large magnetic moment of chromium atoms of 6 μ_B, in contrast to other Bose–Einstein condensates (BECs), magnetic dipole-dipole interaction plays an important role in a chromium BEC. Many new physical properties of degenerate gases arising from these magnetic forces have been predicted in the past and can now be studied experimentally. Besides these phenomena, the large dipole moment leads to a breakdown of standard methods for the creation of a chromium BEC. Cooling and trapping methods had to be adapted to the special electronic structure of chromium to reach the regime of quantum degeneracy. Some of them apply generally to gases with large dipolar forces. We present here a detailed discussion of the experimental techniques which are used to create a chromium BEC and allow us to produce pure condensates with up to 10⁵ atoms in an optical dipole trap. We also describe the methods used to determine the trapping parameters.     

Dynamics of a two-level system coupled to Ohmic bath: a perturbation approach

The quantum dynamics, both non-equilibrium and equilibrium, of the dissipative two-level system is studied by means of the perturbation approach based on a unitary transformation. It works well for the whole parameter range and and our main results are: the coherence-incoherence transition is at ; for the non-equilibrium correlation ; the susceptibility is of a double peak structure for and the Shibas relation is exactly satisfied; at the transition point the equilibrium correlation in the long time limit.Received: 14 October 2003, Published online: 8 June 2004PACS: 72.20.Dp General theory, scattering mechanisms - 05.30.-d Quantum statistical mechanics     

Absorption spectrum of a two-level system in a squeezed vacuum

The weak probe-field absorption spectrum of a two level atom driven by a coherent pump field in a squeezed vacuum is calculated. When the squeezed light and coherent driving field are tuned to atomic resonance, the absorption spectrum of the probe field can show a linewidth smaller than the linewidth in normal vacuum.     

Dynamics of a quantum oscillator strongly and off-resonantly coupled with a two-level system

Beyond the rotating-wave approximation, the dynamics of a quantum oscillator interacting strongly and off-resonantly with a two-level system exhibit beatings, whose period equals the revival time of the two-level system. On a longer time scale, the quantum oscillator shows collapses, revivals and fractional revivals, which are encountered in oscillator observables like the mean number of oscillator quanta and in the two-level inversion population. Also the scattered oscillator field shows doublets with symmetrically displaced peaks.     

A Few-Body Approach to Bose–Einstein Condensation

A simple method to calculate ground state energies for a typical condensates containing up to A ~ 10⁷ atoms is presented. The method, based on the expansion of the wave function in terms of the Faddeev components, which in turn are expanded in terms of potential harmonics is numerically efficient. We obtain ground state results for condensates of ⁸⁷Rb containing up to A → 10⁸ atoms. The results agree very well with other methods in regions where the other methods are valid.     

Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a two-level system

We show that two-photon transport is strongly correlated in one-dimensional waveguide coupled to a two-level system. The exact S matrix is constructed using a generalized Bethe-ansatz technique. We show that the scattering eigenstates of this system include a two-photon bound state that passes through the two-level system as a composite single particle. Also, the two-level system can induce effective attractive or repulsive interactions in space for photons. This general procedure can be applied to the Anderson model as well.     

Excitations in a Dipolar Bose–Einstein Condensate

We study excitations in a dipolar Bose–Einstein condensate with Green’s function. In Bogoliubov approximation, we obtain the dispersion relation. The excitation energy is dependent on the angle between the momentum and the magnetic moment. In the long-wave limit, the dispersion relation reduces to an anisotropic phonon-like dispersion relation.     

Bose condensate drag in a system of two coupled traps

A system of two plane traps disposed one above the other and confined atomic Bose condensate is considered. The possibility of entraining atoms of one of the traps by the atoms of the other trap upon the rotation of the latter is studied. The average angular momentum induced by the rotation of the first trap is found for the atoms in the second trap.     

玻色-爱因斯坦凝聚体干涉效应的数值研究

本文采用辛算法数值求解了GrossPitaevskii (GP) 方程,研究了玻色爱因斯坦凝聚体的干涉现象.讨论了两个凝聚体间以及三个凝聚体间的干涉效应并对两者做了比较,其差异之处我们认为是由增大的凝聚体间的相互作用造成的.     

Bose–Einstein condensation of lithium

7 Li has been studied in a magnetically trapped gas. Many-body quantum theory predicts that the occupation number of the condensate is limited to about 1400 atoms because of the effectively attractive interactions between ⁷Li atoms. Using a versitile phase-contrast imaging technique, we experimentally observe the condensate number to be consistent with this limit. We discuss our measurements, the current theoretical understanding of BEC in a gas with attractive interactions, and future experiments we hope to perform. Received: 4 June 1997     

Steady-state relation of a two-level system strongly coupled to a many-body quantum chaotic environment

We study the long-time average of the reduced density matrix(RDM) of a two-level system as the central system, which is locally coupled to a many-body quantum chaotic system as the environment,under an overall Schr?dinger evolution. A phenomenological relation among elements of the RDM is proposed for a dissipative interaction in the strong coupling regime and is tested numerically with the environment as a defect Ising chain, as well as a mixed-field Ising chain.