One-dimensional Trap Research Articles

Quantum Monte Carlo study of one-dimensional trapped fermions with attractive contact interactions

Using exact continuous quantum Monte Carlo techniques, we study the zero- and finite-temperature properties of a system of harmonically trapped one-dimensional spin1 2 fermions with short-range interactions. Motivated by experimental searches for modulated Fulde-Ferrel-Larkin-Ovchinikov states, we systematically examine the impact of a spin imbalance on the density profiles. We quantify the accuracy of the Thomas-Fermi approximation, finding that for sufficiently large particle numbers N100 it quantitatively reproduces most features of the exact density profile. The Thomas-Fermi approximation fails to capture small Friedel-like spin and density oscillations and overestimates the size of the fully paired region in the outer shell of the trap. Based on our results, we suggest a range of experimentally tunable parameters to maximize the visibility of the double-shell structure of the system and the Fulde-Ferrel-Larkin-Ovchinikov state in the one-dimensional harmonic trap. Furthermore, we analyze the fingerprints of the attractive contact interactions in the features of the momentum and pair momentum distributions.

Exact Solution for a Trapped Fermi Gas with Population Imbalance and BCS Pairing

The problem of a two-component Fermi gas in a harmonic trap, with an imbalanced population and a pairing interaction of zero total momentum, is mapped onto the exactly solvable reduced BCS model. For a one-dimensional trap, the complete ground state diagram is determined with various topological features in ground state energy spectra. In addition to the conventional two-shell density profile of a paired core and polarized outer wings, a three-shell structure as well as a double-peak superfluid distribution are unveiled.

Boson pairs in a one-dimensional split trap

Department of Physics, National University of Ireland, UCC, Cork, Republic of Ireland(Dated: February 1, 2008)We describe the properties of a pair of ultracold bosonic atoms in a one-dimensional harmonictrapping potential with a tunable zero-ranged barrier at the trap centre. The full characterisationof the ground state is done by calculating the reduced single-particle density, the momentum dis-tribution and the two-particle entanglement. We derive several analytical expressions in the limitof infinite repulsion (Tonks-Girardeau limit) and extend the treatment to finite interparticle inter-actions by numerical solution. As pair interactions in double wells form a fundamental buildingblock for many-body systems in periodic potentials, our results have implications for a wide rangeof problems.

Micropatterned electrostatic traps for indirect excitons in coupled GaAs quantum wells

We demonstrate an electrostatic trap for indirect excitons in a field-effect structure based on coupled GaAs quantum wells. Within the plane of a double quantum well indirect excitons are trapped at the perimeter of a SiO2 area sandwiched between the surface of the GaAs heterostructure and a semitransparent metallic top gate. The trapping mechanism is well explained by a combination of the quantum confined Stark effect and local field enhancement. We find the one-dimensional trapping potentials in the quantum well plane to be nearly harmonic with high spring constants exceeding 10 keV/cm^2.

Bose-Einstein condensates under a spatially modulated transverse confinement

We derive an effective nonpolynomial Schrodinger equation (NPSE) for self-repulsive or attractive BEC in the nearly one-dimensional cigar-shaped trap, with the transverse confining frequency period ...

Coherence-Like States of Two Coulomb-Correlated Ions Confinedin a Paul Trap

We report the n×n′ coherence-like state solutions in the casesof n,n′ = 1,2,… for the system including two Coulomb-correlatedions confined in a one-dimensional Paul trap with a time-dependentharmonic potential. One of the n′ exact solutions of thecentre-of-mass motion describes a generalized coherent state. For asmall driving strength the n approximate solutions of relative motionare constructed, which describe the coherent oscillations of the twoions around the classical equilibrium position.

Energy band structure of two ions in a one-dimensional Paul trap

Making use of the well-known truncated-series method, we give a numerical program to calculate the exact solutions of two Coulomb-correlated ions confined in a linear Paul trap. The discrete motion state functions and energy spectra are obtained for the trap frequencies approaching the experimentally realizable limiting values, which correspond to a denumerable infinite point-set of the frequencies. Continuously varying the trap frequency between two neighboring points of the denumerable infinite set, from the quantum perturbation technique we find the energy-band structure based on the exact discrete spectra in which the bands are narrower and the gaps wider. The band structure can influence the laser cooling of Paul trapped ions and the quantum logic operation based on the system that should be considered in the corresponding experiments thereby.

The Behaviour of Aging Functions in One-Dimensional Bouchaud's Trap Model

Let τ i be a collection of i.i.d. positive random variables with distribution in the domain of attraction of an α-stable law with α<1. The symmetric Bouchaud's trap model on ℤ is a Markov chain X(t) whose transition rates are given by w xy =(2τ x )−1 if x, y are neighbours in ℤ. We study the behaviour of two correlation functions: ℙ[X(t w +t)=X(t w )] and Open image in new window It is well known that for any of these correlation functions a time-scale t=f(t w ) such that aging occurs can be found. We study these correlation functions on time-scales different from f(t w ), and we describe more precisely the behaviour of a singular diffusion obtained as the scaling limit of Bouchaud's trap model.

Landau Dynamics of a Grey Soliton in a Trapped Condensate

It is shown that grey soliton dynamics in a one-dimensional trap can be treated within the framework of the local density approximation as Landau dynamics of a quasiparticle. A soliton of arbitrary amplitude moves in the trapping potential without deformation of its density profile as a particle of mass 2m. The dynamics in the local density approximation is shown to be consistent with the perturbation theory for dark solitons. Dynamics of a vortex ring in a trap is discussed qualitatively.

Quantum effects in a one-dimensional magnetic gravitational trap for ultracold neutrons

The problem of storing ultracold neutrons over a plane magnetic mirror in the presence of gravity is considered. For neutrons with a definite polarization, the sum of the magnetic and gravitational potentials can have a minimum and, hence, form a magnetic gravitational trap. For low energies of vertical motion, the neutron state in this well is quantized. The possibility of accomplishing the corresponding quantum gravitational experiment is analyzed.

Low-dimensional Bose-Einstein condensation in finite-number trapped atoms

The effect of finite number of trapped atoms is discussed in Bose-Einstein condensation without interaction, according to Thomas-Fermi approximation. We obtain the state density by high-temperature expansion and calculate the critical temperature in one-dimensional(1D) and two-dimensional(2D) trap potentials. Then the temperature dependence of specific heat are analyzed. The results show that: in 2D case, the specific heat c is proportional to T2; in 1D case,c increases linearly with temperature.

Anomalous diffusion, localization, aging, and subaging effects in trap models at very low temperature.

We study in detail the dynamics of the one-dimensional symmetric trap model via a real-space renormalization procedure which becomes exact in the limit of zero temperature. In this limit, the diffusion front in each sample consists of two delta peaks, which are completely out of equilibrium with each other. The statistics of the positions and weights of these delta peaks over the samples allows to obtain explicit results for all observables in the limit T-->0. We first compute disorder averages of one-time observables, such as the diffusion front, the thermal width, the localization parameters, the two-particle correlation function, and the generating function of thermal cumulants of the position. We then study aging and subaging effects: our approach reproduces very simply the two different aging exponents and yields explicit forms for scaling functions of the various two-time correlations. We also extend the real-space renormalization group method to include systematic corrections to the previous zero temperature procedure via a series expansion in T. We then consider the generalized trap model with parameter alpha in [0,1] and obtain that the large scale effective model at low temperature does not depend on alpha in any dimension, so that the only observables sensitive to alpha are those that measure the "local persistence," such as the probability to remain exactly in the same trap during a time interval. Finally, we extend our approach at a scaling level for the trap model in d=2 and obtain the two relevant time scales for aging properties.

Erratum: Diffusion-limited reaction for the one-dimensional trap system [Phys. Rev. E67, 056123 (2003)

Erratum: Diffusion-limited reaction for the one-dimensional trap system [Phys. Rev. E<b>67</b>, 056123 (2003)

Mean-field model for Josephson oscillation in a Bose-Einstein condensate on an one-dimensional optical trap

Using the axially-symmetric time-dependent Gross-Pitaevskii equation we study the phase coherence in a repulsive Bose-Einstein condensate (BEC) trapped by a harmonic and an one-dimensional optical lattice potential to describe the experiment by Cataliotti {\it et al.} on atomic Josephson oscillation [Science {\bf 293}, 843 (2001)]. The phase coherence is maintained after the BEC is set into oscillation by a small displacement of the magnetic trap along the optical lattice. The phase coherence in the presence of oscillating neutral current across an array of Josephson junctions manifests in an interference pattern formed upon free expansion of the BEC. The numerical response of the system to a large displacement of the magnetic trap is a classical transition from a coherent superfluid to an insulator regime and a subsequent destruction of the interference pattern in agreement with the more recent experiment by Cataliotti {\it et al.} [e-print cond-mat/0207139].

Linear and nonlinear response in the aging regime of the one-dimensional trap model

We investigate the behavior of the response function in the one-dimensional trap model using scaling arguments that we confirm by numerical simulations. We study the average position of the random walk at time t(w)+t, given that a small bias h is applied at time t(w). Several scaling regimes are found, depending on the relative values of t, t(w), and h. Comparison with the diffusive motion in the absence of bias allows us to show that the fluctuation-dissipation relation is valid even in the aging regime, at least for times such that linear response is obeyed. However, for sufficiently long times, the response always becomes nonlinear in h.

Diffraction-limited optical dipole trap with a hollow optical fiber

We propose a novel three-dimensional diffraction-limited far-off-resonance optical dipole trap (DFORT) for neutral atoms operating in the Lamb–Dicke regime. Such a microscopic DFORT is generated by the diffracted LP01 mode of a hollow-core optical fiber near the fiber facet. For 87Rb and 133Cs atoms, we estimate that with a 100-mW trap-laser power, a cigar-shaped far-off-resonance optical dipole trap provides potential depth U0≃10 mK, radial (axial) trap frequency fr≃100 kHz(fz≃10 kHz), and trap volume Vtrap≃104λ3. The DFORT has the unique feature of a tightly focused trap with a large trap volume and convenient loading and cooling of the precooled atoms, which may be useful for optical Bose–Einstein condensation. A DFORT may be also operated as an elongated one-dimensional optical trap.

Breathing mode collective excitation of a Bose–Einstein condensate in a low-dimensional trap

Using a sum-rule method and a time-dependent variational method, we study the breathing mode collective-excitation frequency of a trapped Bose–Einstein condensate. We show that the general result for a three-dimensional trap correctly goes over to purely two- or one-dimensional limit. In the case of a realistic two- or one-dimensional trap, we obtain the lowest order correction for the collective-excitation frequency due to the finiteness of the trap frequency in the tightly trapped direction. We also show numerical results for the collective-excitation frequencies using parameters relevant to recent experiments.

Subdiffusion and localization in the one-dimensional trap model.

We study a one-dimensional generalization of the exponential trap model using both numerical simulations and analytical approximations. We obtain the asymptotic shape of the average diffusion front in the subdiffusive phase. Our central result concerns the localization properties. We find the dynamical participation ratios to be finite, but different from their equilibrium counterparts. Therefore, the idea of a partial equilibrium within the limited region of space explored by the walk is not exact, even for long times where each site is visited a very large number of times. We discuss the physical origin of this discrepancy, and characterize the full distribution of dynamical weights. We also study two different two-time correlation functions, which exhibit different aging properties: one is "sub aging" whereas the other one shows "full aging," therefore, two diverging time scales appear in this model. We give intuitive arguments and simple analytical approximations that account for these differences, and obtain new predictions for the asymptotic (short-time and long-time) behavior of the scaling functions. Finally, we discuss the issue of multiple time scalings in this model.

Exact ground-state number fluctuations of trapped ideal and interacting fermions

We consider a small and fixed number of fermions in an isolated one-dimensional trap (microcanonical ensemble). The ground state of the system is defined at T=0, with the lowest single-particle levels occupied. The number of particles in this ground state fluctuates as a function of excitation energy. By breaking up the energy spectrum into particle and hole sectors, and mapping the problem onto the classic number partitioning theory, we formulate a new method to calculate the exact particle number fluctuation more efficiently than the direct combinatorics method. The exact ground state number fluctuation for particles interacting via an inverse-square pair-wise interaction is also calculated.

Perturbation theory for the one-dimensional trapping reaction

We consider the survival probability of a particle in the presence of a finite number of diffusing traps in one dimension. Since the general solution for this quantity is not known when the number of traps is greater than two, we devise a perturbation series expansion in the diffusion constant of the particle. We calculate the persistence exponent associated with the particle's survival probability to second order and find that it is characterised by the asymmetry in the number of traps initially positioned on each side of the particle.