冷原子物理中的一维少体问题

作为构成量子多体系统的基本单元,一维少体系统的研究不仅可以在理论上为多体系统的量子关联及动力学等性质提供更为基本的理解,也可以为实验上制备多体系统提供更加方便和功能更加全面的方法.本文回顾了冷原子物理中一维少体系统最新的实验和理论进展.首先介绍了少体实验中实现的谐振子势阱中确定原子数的精确制备,亚稳态势阱和双阱系统中原子的隧穿,以及强相互作用下等效自旋链的实验结果.然后深度解析了理论研究方面,特别是基于精确可解模型的一些重要结果,包括亚稳态势阱中相互作用原子的隧穿概率,以及相应实验上常见势阱的能谱分析、密度分布、隧穿动力学以及强相互作用极限下的有效自旋链模型等.     

Nonclassicality generated by propagation of atoms through a cavity field

We successively pass two V-type three-level atoms through a single-mode cavity field. Considering the field to be initially in a classical state, we evaluate various statistical properties such as the quasiprobability Q function, Wigner distribution, Mandel?s Q parameter and normal squeezing of the resulted field. We notice that the sequential crossing of atoms induces nonclassicality into the character of a pure classical state (coherent field). The initial thermal field shows sub-Poissonian as well as squeezing property after interacting with the V atoms.     

Bose-einstein condensation in trapped dipolar gases

We discuss Bose-Einstein condensation in a trapped gas of bosonic particles interacting dominantly via dipole-dipole forces. We find that in this case the mean-field interparticle interaction and, hence, the stability diagram are governed by the trapping geometry. Possible physical realizations include ultracold heteronuclear molecules, or atoms with laser induced electric dipole moments.     

Bistability of radiation force on N-atom system

We consider a system with N two-level atoms in a cavity, interacting with an external radiation field. Using Ehrenfest's theorem the radiation force on the N-atom system is studied as a function of the external radiation field. In a certain parameter region we are able to show that the radiation force can be bistable     

Creation of atomic W state in a cavity by adiabatic passage

We propose two relatively robust schemes to generate controllable (deterministic) atomic W states of three Λ-like atoms interacting with an optical cavity and a laser beam. Losses due to atomic spontaneous emissions and to cavity decay are efficiently suppressed by employing adiabatic passage technique and appropriately designed atom-field couplings. In these schemes the three atoms traverse the cavity-mode and the laser beam and become entangled in the free space outside the cavity.     

Quantification of Quantum Entanglement in a Multiparticle System of Two-Level Atoms Interacting with a Squeezed Vacuum State of the Radiation Field

We quantify multiparticle quantum entanglement in a system of N two-level atoms interacting with a squeezed vacuum state of the electromagnetic field. We calculate the amount of quantum entanglement present among one hundred such two-level atoms and also show the variation of that entanglement with the radiation field parameter. We show the continuous variation of the amount of quantum entanglement as we continuously increase the number of atoms from N = 2 to N = 100. We also discuss that the multiparticle correlations among the N two-level atoms are made up of all possible bipartite correlations among the N atoms.     

Atom-dimer and dimer-dimer scattering in fermionic mixtures near a narrow Feshbach resonance

We develop a diagrammatic approach for solving few-body problems in heteronuclear fermionic mixtures near a narrow interspecies Feshbach resonance. We calculate s-, p-, and d-wave phaseshifts for the scattering of an atom by a weakly-bound dimer. The fermionic statistics of atoms and the composite nature of the dimer lead to a strong angular momentum dependence of the atom-dimer interaction, which manifests itself in a peculiar interference of the scattered s- and p-waves. This effect strengthens with the mass ratio and is remarkably pronounced in ⁴⁰K-(⁴⁰K-⁶Li) atom-dimer collisions. We calculate the scattering length for two dimers formed near a narrow interspecies resonance. Finally, we discuss the collisional relaxation of the dimers to deeply bound states and evaluate the corresponding rate constant as a function of the detuning and collision energy.     

A Method for DeterminingB1Field Inhomogeneity. Are the Biases Assumed in Heteronuclear Relaxation Experiments Usually Underestimated?

We describe a method allowing the determination of the effectiveB₁field amplitude distribution in a high-resolution NMR spectrometer. This method which can be adapted to almost any sequence, essentially consists of a nutation followed by a purgingB₀gradient pulse. Experimental results obtained with this approach are described in homonuclear and heteronuclear cases. The experimental distributions are used to estimate the biases induced byB₁inhomogeneity, as well as the loss of RF power on heteronuclear transverse self-relaxation rate determination. In this type of measurement, the experimental biases induced on the intensities can be as large as 5% for long mixing times.     

Atomic coherent states and reduced quantum fluctuations in optical transients

We show that the atomic coherent states (the Bloch states) commonly encountered in coherent transient phenomena exhibit squeezing. We illustrate this property calculating the degree of squeezing and the normalized correlation coefficient g⁽²⁾ for a system of N two-level atoms interacting with a cw laser electric field.     

Single-atom entropy squeezing for two two-level atoms interacting with a single-mode radiation field

In this paper we consider a system of two two-level atoms interacting with a single-mode quantized electromagnetic field in a lossless resonant cavity via l-photon-transition mechanism. The field and the atoms are initially prepared in the coherent state and the excited atomic states, respectively. For this system we investigate the entropy squeezing, the atomic variances, the von Neumann entropy and the atomic inversions for the single-atom case. Also we comment on the relationship between spin squeezing and linear entropy. We show that the amounts of the nonclassical effects exhibited in the entropy squeezing for the present system are less than those produced by the standard Jaynes-Cummings model. The entropy squeezing can give information on the corresponding von Neumann entropy. Also the nonclassical effects obtained from the asymmetric atoms are greater than those obtained from the symmetric ones. Finally, the entropy squeezing gives better information than the atomic variances only for the asymmetric atoms.     

Scanning tunneling microscopy of the nonequilibrium interaction of impurity states at semiconductor surfaces

Interaction of two localized impurity states of Si atoms at a GaAs surface was studied by scanning tunneling microscopy and spectroscopy. The effects of a twofold “switching” on and off of the states of each of the interacting atoms, the tunneling-interaction-induced mutual level pulling of these states, and the level stabilization near E _F were observed. These effects are explained in terms of the extended Anderson model.     

Non-universal Fermi polaron in quasi two-dimensional quantum gases

We consider an impurity problem in a quasi-two-dimensional Fermi gas, where a spin-down impurity is immersed in a Fermi sea of N spin-up atoms. Using a variational approach and an effective two-channel model, we obtain the energy for a wide range of interaction strength and for various different mass ratios between the impurity and the background fermion in the context of heteronuclear mixture. We demonstrate that in a quasi-two-dimensional Fermi gas there exists a transition of the ground state from polaron in the weakly interacting region to molecule in the strongly interacting region. The critical interaction strength of the polaron-molecule transition is non-universal and depends on the particle density of the background Fermi sea. We also investigate the excited repulsive polaron state, and find similar non-universal behavior.     

Controlling quantum discord dynamics in cavity QED systems by applying a classical driving field with phase decoherence

We investigate a two-level atom interacting with a quantized cavity field and a classical driving field in the presence of phase decoherence and find that a stationary quantum discord can arise in the interaction of the atom and cavity field as the time turns to infinity. We also find that the stationary quantum discord can be increased by applying a classical driving field. Furthermore, we explore the quantum discord dynamics of two identical non-interacting two-level atoms independently interacting with a quantized cavity field and a classical driving field in the presence of phase decoherence. Results show that the quantum discord between two atoms is more robust than entanglement under phase decoherence and the classical driving field can help to improve the amount of quantum discord of the two atoms.     

Controlling quantum discord dynamics in cavity QED systems by applying a classical driving field with phase decoherence

We investigate a two-level atom interacting with a quantized cavity field and a classical driving field in the presence of phase decoherence and find that a stationary quantum discord can arise in the interaction of the atom and cavity field as the time turns to infinity.We also find that the stationary quantum discord can be increased by applying a classical driving field.Furthermore,we explore the quantum discord dynamics of two identical non-interacting two-level atoms independently interacting with a quantized cavity field and a classical driving field in the presence of phase decoherence.Results show that the quantum discord between two atoms is more robust than entanglement under phase decoherence and the classical driving field can help to improve the amount of quantum discord of the two atoms.     

Quantum Recoil Effects of Spontaneous Emission on Disentanglement

By taking into account spatial degrees of freedom of atoms, we study theinternal-state disentanglement dynamics of two atoms interacting with avacuum multi-mode noise field. We show that the complete internal-statedisentanglement of the two atoms, caused due to the atomic spontaneousemission can be achieved in a finite time.     

Cooperative effects in the two atom resonance fluorescence spectrum

We consider the resonance fluorescence spectrum of two similar interacting atoms in the limit of high photon densities. The excitation spectrum of the symmetric modes contains two sidebands in addition to the usual three peaks which are analogous to those of the isolated atom. These two new sidebands are due entirely to the cooperative behaviour of the two atoms and vanish when the atoms are far apart. The energy shifts and spectral widths for these two sidebands are two and five times larger than those for the isolated atom respectively. The probability of occurrence of these sidebands depends on the parameters V_AB/Ω and γ²₀/Ω², where V_AB is the dipole-dipole interaction energy, γ₀ is the spontaneous emission probability and Ω is the Rabi frequency. The asymmetric broadening of both sidebands depends on the parameter γ₀/Ω. The possibility to measure the dipole-dipole energy through the observation of these sidebands is discussed.     

Spin singlet mott states and evidence for spin singlet quantum condensates of spin-one bosons in lattices

We have investigated spin singlet Mott states of spin-one bosons with antiferromagnetic interactions. These spin singlet states do not break rotational symmetry and exhibit remarkably different macroscopic properties compared with nematic Mott states of spin-one bosons. We demonstrate that the dynamics of spin singlet Mott states is fully characterized by even- or odd-class quantum dimer models. The difference between spin singlet Mott states for even and odd numbers of atoms per site can be attributed to a selection rule in the low energy sectors of on-site Hilbert spaces; alternatively, it can also be attributed to an effect of Berry’s phases on bosonic Mott states. We also discuss evidence for spin singlet quantum condensate of spin-one atoms. Our main finding is that in a projected spin singlet Hilbert space, the low energy physics of spin-one bosons is equivalent to that of a Bose-Hubbard model for spinless bosons interacting via Ising gauge fields. The other major finding is spin-charge separation in some one-dimensional Mott states. We propose charge-e spin singlet superfluid for an odd number of atoms per lattice site and charge-2e spin singlet superfluid for an even number of atoms per lattice site in one-dimensional lattices. All discussions in this article are limited to integer numbers of bosons per site.     

Efficient generation and control of robust stationary light signals in a double-Λ system of cold atoms

We study the dynamic processes of reversible light storage in a double-Λ system of cold atoms by modulating two counter-propagating control fields in three successive stages. We find that stationary light pulses (SLPs) can be generated when we switch on both control fields to retrieve the stored light signal from a wave-packet of atomic spin coherence. But the two control fields should have equal Rabi frequencies for a symmetric structure of atomic levels while unequal Rabi frequencies for an asymmetric structure of atomic levels. That is, the generation of SLPs requires a special ratio between Rabi frequencies of the two control fields, which is determined by the spontaneous decay rates of relevant atomic transitions. We also show that phase modulation and profile reversal of the released light signal can be implemented by suitably manipulating the two control fields. The double-Λ system of cold atoms has the advantage of high efficiency and high fidelity, when compared to the Λ system of cold atoms, because SLPs generated therein suffer very slow decay and diffusion.     

Quantum Treatment of the Interaction Between an N-Level Atom and Two Noninteracting Two-Level Atoms

We consider the problem of two two-level atoms interacting with N-level atom. We obtain the exact solution for the wave function for the case where both atoms are identical and the system is treated at exact resonance. We use the results obtained for discussing the temporal evolution of the atomic inversion, in particular, the collapse and revival phenomena. We build up our discussion on the variation of the atomic number j and the atomic angle θ. For small j, the system exhibits a small period of collapse, and for large j we observe a long period of revival. We employ the linear entropy in the discussion of entanglement. We show that the atomic angle θ influences the system in such a way that the period of partial entanglement increases with increase in the value of θ. In addition to the variance squeezing, we also examine the entanglement between the spinors and show that the squeezing phenomenon occurs in the second quadrature, being absent in the first quadrature. Also we realize that the squeezing phenomenon reaches its maximum and gets more pronounced for a small value of the atomic number and a large value of the atomic angle.     

Effective Field Theory Analysis of Three-Boson Systems at Next-To-Next-To-Leading Order

We use an effective field theory for short-range forces (SREFT) to analyze systems of three identical bosons interacting via a two-body potential that generates a scattering length, a, which is large compared to the range of the interaction, ?. The amplitude for the scattering of one boson off a bound state of the other two is computed to next-to-next-to-leading order (N²LO) in the ?/a expansion. At this order, two pieces of three-body data are required as input in order to renormalize the amplitude (for fixed a). We apply our results to a model system of three Helium-4 atoms, which are assumed to interact via the TTY potential. We generate N²LO predictions for atom-dimer scattering below the dimer breakup threshold using the bound-state energy of the shallow Helium-4 trimer and the atom-dimer scattering length as our two pieces of three-body input. Based on the convergence pattern of the SREFT expansion, as well as differences in the predictions of two renormalization schemes, we conclude that our N²LO phase- shift predictions will receive higher-order corrections of < 0.2 %. In contrast, the prediction of SREFT for the binding energy of the “deep” trimer of Helium-4 atoms displays poor convergence.