Periodic Optical Potential Research Articles

Giant and tunable Goos-Hänchen shift with a high reflectance induced by PT-symmetry in atomic vapor.

The Goos-Hänchen (GH) shifts of light beams reflected from conventional passive optical systems could be enhanced using the Brewster angle effect or resonance effect, but the maximum GH shift is located at the reflectance minima, which is difficult for experimental detection. In this paper, we present an efficient and flexible scheme to realize complex parity-time (PT)-symmetric periodic optical potentials (complex crystals) in helium atomic vapor. The GH shifts of probe light reflected from the complex crystal are theoretically investigated and large GH shifts could be obtained inside the high-reflection band. When the complex crystal is operated near the coherent perfect absorption-laser point, the maximum GH shift of probe light is exactly located at the reflectance peak. Moreover, the GH shifts could be easily controlled by adjusting the intensity of control light.

Energetics of critical oscillators in active bacterial baths

We investigate the nonequilibrium energetics near a critical point of a non-linear oscillator immersed in an active bacterial bath. At the critical point, we reveal a scaling exponent of the average power exerted by a constant non-conservative torque , where D a is the effective diffusivity and τ the correlation time of the bacterial bath described by a Gaussian colored noise. Other features that we investigate are the average stationary power and the variance of the work both below and above the saddle-node bifurcation. Above the bifurcation, the average power attains an optimal, minimum value for finite τ that is below its zero-temperature limit. Furthermore, we reveal a finite-time uncertainty relation for active matter which leads to values of the Fano factor of the work that can be below 2k B T eff, with T eff the effective temperature of the oscillator in the bacterial bath. We analyze different Markovian approximations to describe the nonequilibrium stationary state of the system. Finally, we illustrate our results in the experimental context by considering the example of driven colloidal particles in periodic optical potentials within an E. Coli bacterial bath.

Asymptotic behavior of correlation functions of one-dimensional polar-molecules on optical lattices

We combine a slave-spin approach with a mean-field theory to develop an approximate theoretical scheme to study the density, spin, and, pairing correlation functions of fermionic polar molecules. We model the polar molecules subjected to a one-dimensional periodic optical lattice potential using a generalized t–J model, where the long-range part of the interaction is included through the exchange interaction parameter. For this model, we derive a set of self-consistent equations for the correlation functions, and evaluate them numerically for the long-distance behavior. We find that the pairing correlations are related to spin correlations through the density and the slave-spin correlations. Further, our calculations indicates that the long-range character of the interaction can be probed through these correlation functions. In the absence of exact solutions for the one-dimensional t–J model, our approximate theoretical treatment can be treated as a useful tool to study one dimensional long-range correlated fermions.

Spectral analysis of the Schrödinger operator with a PT-symmetric periodic optical potential

In this paper, we give a description of the spectral analysis of the Schrödinger operator L(q) with the potential q(x) = 4 cos2 x + 4iV sin 2x for all V > 1/2. First, we consider the Bloch eigenvalues and spectrum of L(q). Then, we investigate spectral singularities and essential spectral singularities (ESS). We prove that there exists a sequence V2 < V3 < ⋯ such that the operator L(q) has no ESS and has ESS, respectively, if and only if V ≠ Vk and V = Vk for k ≥ 2, where Vk → ∞ as k → ∞, V2 is the second critical point. Using ESS, we classify the spectral expansion in term of the points Vk for k ≥ 2. Finally, we discuss the critical points Vk, formulate some conjectures, and describe the changes in the spectrum of L(q) when V changes from 1/2 to ∞.

Parity-time symmetry light bullets in a cold Rydberg atomic gas.

A scheme is proposed to generate stable light bullets (LBs) in a cold Rydberg atomic system with a parity-time (PT) symmetric potential, by utilizing electromagnetically induced transparency (EIT). Using an incoherent population pumping between two low-lying levels and spatial modulations of control and auxiliary laser fields, we obtain a two-dimensional (2D) periodic optical potential with PT symmetry. Based on PT symmetry potential and the long-range Rydberg-Rydberg atomic interaction, the system may support slow LBs with low light intensity. Further, it is found that the local and non-local nonlinear coefficients and PT-symmetric potential can be tuned and used to manipulate the behavior of LBs.

Measuring the Hydrodynamic Linear Response of a Unitary Fermi Gas.

We directly observe the hydrodynamic linear response of a unitary Fermi gas confined in a box potential and subject to a spatially periodic optical potential that is translated into the cloud at speeds ranging from subsonic to supersonic. We show that the time-dependent change of the density profile is sensitive to the thermal conductivity, which controls the relaxation rate of the temperature gradients and hence the responses arising from adiabatic and isothermal compression.

Parity-time symmetry along with nonlocal optical solitons and their active controls in a Rydberg atomic gas

We propose a scheme to realize parity-time ($\mathcal{PT}$) symmetry and nonlocal optical solitons in a cold Rydberg atomic system with electromagnetically induced transparency. We show that a two-dimensional (2D) periodic optical potential with $\mathcal{PT}$ symmetry can be obtained for the propagation of probe laser field by using an incoherent population pumping between two low-lying levels and spatial modulations of control and assistant laser fields. We also show that, based on the giant nonlocal Kerr nonlinearity originated from the strong, long-range atom-atom interaction, the system supports 2D nonlocal gap solitons with very low light intensity. In particular, we find that the degree of the nonlocality of the Kerr nonlinearity, which can be actively tuned in our system, can be used to manipulate the phase transition of the $\mathcal{PT}$ symmetry and the behavior of the nonlocal optical solitons. Our study opens a route for developing non-Hermitian nonlinear optics, especially for realizing and controlling high-dimensional weak-light optical solitons through adjustable $\mathcal{PT}$ symmetry and giant nonlocal optical nonlinearity.

Metal-insulator-superconductor transition of spin-3/2 atoms on optical lattices

We use a slave-rotor approach within a mean-field theory to study the competition of metallic, Mott-insulating, and superconducting phases of spin-3/2 fermions subjected to a periodic optical lattice potential. In addition to the metallic, the Mott-insulating, and the superconducting phases that are associated with the gauge symmetry breaking of the spinon field, we identify a novel emerging superconducting phase that breaks both roton and spinon field gauge symmetries. This novel superconducting phase emerges as a result of the competition between spin-0 singlet and spin-2 quintet interaction channels naturally available for spin-3/2 systems. The two superconducting phases can be distinguished from each other by quasiparticle weight. We further discuss the properties of these phases for both two-dimensional square and three-dimensional cubic lattices at zero and finite temperatures.

The spectrum of the Hamiltonian with a PT-symmetric periodic optical potential

We give a complete description, provided with a mathematical proof, of the shape of the spectrum of the Hill operator with potential [Formula: see text], where [Formula: see text] We prove that the second critical point [Formula: see text], after which the real parts of the first and second bands disappear, is a number between [Formula: see text] and [Formula: see text]. Moreover, we prove that [Formula: see text] is the degeneration point for the first periodic eigenvalue. Besides, we give a scheme by which one can find arbitrary precise value of the second critical point as well as the [Formula: see text]th critical points after which the real parts of the [Formula: see text]th and [Formula: see text]th bands disappear, where [Formula: see text]

Composite device for interfacing an array of atoms with a single nanophotonic cavity mode

We propose a method of trapping atoms in arrays near to the surface of a composite nanophotonic device with optimal coupling to a single cavity mode. The device, comprised of a nanofiber mounted on a grating, allows the formation of periodic optical trapping potentials near to the nanofiber surface along with a high cooperativity nanofiber cavity. We model the device analytically and find good agreement with numerical simulations. We numerically demonstrate that for an experimentally realistic device, an array of traps can be formed whose centers coincide with the antinodes of a single cavity mode, guaranteeing optimal coupling to the cavity. Additionally, we simulate a trap suitable for a single atom within 100 nm of the fiber surface, potentially allowing larger coupling to the nanofiber than found using typical guided mode trapping techniques.

Properties of spin–orbit-coupled Bose–Einstein condensates

The experimental and theoretical research of spin–orbit-coupled ultracold atomic gases has advanced and expanded rapidly in recent years. Here, we review some of the progress that either was pioneered by our own work, has helped to lay the foundation, or has developed new and relevant techniques. After examining the experimental accessibility of all relevant spin–orbit coupling parameters, we discuss the fundamental properties and general applications of spin–orbit-coupled Bose–Einstein condensates (BECs) over a wide range of physical situations. For the harmonically trapped case, we show that the ground state phase transition is a Dicke-type process and that spin–orbit-coupled BECs provide a unique platform to simulate and study the Dicke model and Dicke phase transitions. For a homogeneous BEC, we discuss the collective excitations, which have been observed experimentally using Bragg spectroscopy. They feature a roton-like minimum, the softening of which provides a potential mechanism to understand the ground state phase transition. On the other hand, if the collective dynamics are excited by a sudden quenching of the spin–orbit coupling parameters, we show that the resulting collective dynamics can be related to the famous Zitterbewegung in the relativistic realm. Finally, we discuss the case of a BEC loaded into a periodic optical potential. Here, the spin–orbit coupling generates isolated flat bands within the lowest Bloch bands whereas the nonlinearity of the system leads to dynamical instabilities of these Bloch waves. The experimental verification of this instability illustrates the lack of Galilean invariance in the system.

Dipolar Bose–Einstein condensates in triple-well potentials

Dipolar Bose–Einstein condensates in triple-well potentials are well-suited model systems for periodic optical potentials with important contributions of the non-local and anisotropic dipole–dipole interaction, which show a variety of effects such as self-organization and formation of patterns. We address here a macroscopic sample of dipolar bosons in the mean-field limit. This work is based on the Gross–Pitaevskii description of dipolar condensates in triple-well potentials by Peter et al (2012 J. Phys. B: At. Mol. Opt. Phys. 45 225302). Our analysis goes beyond the calculation of ground states presented there and clarifies the role of excited and metastable states in such systems. In particular, we find the formation of phases originating from the interplay of several states with distinct stability properties. As some of the phases are formed by metastable states, special attention is paid to the characteristics of phase transitions in real time and the dynamical stabilization of the condensate.

Bragg scattering and Brownian motion dynamics in optically induced crystals of submicron particles

A set of four confocal laser beams of 1064-nm wavelength is used to prepare optically induced crystals of submicron particles in aqueous solution. Thousands of polystyrene spheres of about 200 nm in diameter are trapped in three dimensions. Bragg scattering patterns obtained with a probe beam of 532-nm wavelength are in agreement with the calculated lattice structure and its polarization dependence. The decay and rise of the Bragg scattering intensity upon switching the lattice off and on reveal the Brownian motion dynamics of the particles in the periodic optical trapping potential. Experimental results agree well with results from trajectory simulations based on the Langevin equation. The results exhibit the interplay between Brownian motion and deterministic forces in an inhomogeneous (near-)periodic optical trapping potential.

One-dimensional array of ion chains coupled to an optical cavity

We present a novel system where an optical cavity is integrated with a microfabricated planar-electrode ion trap. The trap electrodes produce a tunable periodic potential allowing the trapping of up to 50 separate ion chains aligned with the cavity and spaced by 160 μm in a one-dimensional array along the cavity axis. Each chain can contain up to 20 individually addressable Yb+ ions coupled to the cavity mode. We demonstrate deterministic distribution of ions between the sites of the electrostatic periodic potential and control of the ion–cavity coupling. The measured strength of this coupling should allow access to the strong collective coupling regime with ≲10 ions. The optical cavity could serve as a quantum information bus between ions or be used to generate a strong wavelength-scale periodic optical potential.

Double symmetry breaking of solitons in one-dimensional virtual photonic crystals

We demonstrate that spatial solitons undergo two consecutive spontaneous symmetry breakings (SSBs), with the increase of the total power, in nonlinear photonic crystals (PhCs) built as arrays of alternating linear and nonlinear stripes, in the case when the maxima of the effective refractive index coincide with the minima of the self-focusing coefficient and vice versa (i.e., the corresponding linear and nonlinear periodic potentials are in competition). This setting may be induced, as a virtual PhC, by means of the electromagnetically induced-transparency (EIT) technique, in a uniform optical medium. It may also be realized as a Bose-Einstein condensate (BEC) subject to the action of the combined periodic optical potential and periodically modulated Feshbach resonance. The first SSB happens at the center of a linear stripe, pushing a broad low-power soliton into an adjacent nonlinear stripe and gradually suppressing side peaks in the soliton's shape. Then the soliton restores its symmetry, being pinned to the midpoint of the nonlinear stripe. The second SSB occurs at higher powers, pushing the narrow soliton off the center of the nonlinear channel, while the soliton keeps its internal symmetry. The results are obtained by means of numerical and analytical methods. They may be employed to control switching of light beams by means of the varying power.

Quantum Machine Using Cold Atoms

For a machine to be useful in practice, it preferably has to meet two requirements: namely, (i) to be able to perform work under a load and (ii) its operational regime should ideally not depend on the time at which the machine is switched-on. We devise a minimal setup, consisting of two atoms only, for an ac-driven quantum motor which fulfills both these conditions. Explicitly, the motor consists of two different interacting atoms placed into a ring-shaped periodic optical potential -- an optical "bracelet" --, resulting from the interference of two counter-propagating Laguerre-Gauss laser beams. This bracelet is additionally threaded by a pulsating magnetic flux. While the first atom plays a role of a quantum "carrier", the second serves as a quantum "starter", which sets off the "carrier" into a steady rotational motion. For fixed zero-momentum initial conditions the asymptotic carrier velocity saturates to a unique, nonzero value which becomes increasingly independent on the starting time with increasing "bracelet"-size. We identify the quantum mechanisms of rectification and demonstrate that our quantum motor is able to perform useful work.

Universal Behavior of Pair Correlations in a Strongly Interacting Fermi Gas

We show that short-range pair correlations in a strongly interacting Fermi gas follow a simple universal law described by Tan's relations. This is achieved through measurements of the static structure factor which displays a universal scaling proportional to the ratio of Tan's contact to the momentum C/q. Bragg spectroscopy of ultracold 6Li atoms from a periodic optical potential is used to measure the structure factor for a wide range of momenta and interaction strengths, providing broad confirmation of this universal law. We calibrate our Bragg spectra using the f-sum rule, which is found to improve the accuracy of the structure factor measurement.

Effective mass approach for a Bose-Einstein condensate in an optical lattice

We study the stationary and propagating solutions for a Bose-Einstein condensate (BEC) in a periodic optical potential with an additional confining optical or magnetic potential. Using an effective mass approximation we express the condensate wave function in terms of slowly-varying envelopes modulating the Bloch modes of the optical lattice. In the limit of a weak nonlinearity, we derive a nonlinear Schrodinger equation for propagation of the envelope function which does not contain the rapid oscillation of the lattice. We then consider the ground state solutions in detail in the regime of weak, moderate and strong nonlinear interactions. We describe the form of solution which is appropriate in each regime, and place careful limits on the validity of each type of solution. Finally we extend the study to the propagating dynamics of a spinor atomic BEC in an optical lattice and some interesting phenomena are revealed.

Effects of periodic optical lattice potential on dark solitons in a Bose–Einstein condensate

This paper investigates the dynamics of dark solitons in a Bose–Einstein condensate with a magnetic trap and an optical lattice (OL) trap, and analyses the effects of the periodic OL potential on the dynamics by applying the variational approach based on the renormalized integrals of motion. The results show that the dark soliton becomes only a standing-wave and free propagation of the dark soliton is not possible when the periodic length of the OL potential is approximately equal to the effective width of the dark soliton. When the periodic length is very small or very large, the effects of the OL potential on the dark soliton will be sharply reduced. Finally, the numerical results confirm these theoretical findings.

Caustic formation in expanding condensates of cold atoms

We study the evolution of density in an expanding Bose-Einstein condensate that initially has a spatially varying phase, concentrating on behavior when these phase variations are large. In this regime large density fluctuations develop during expansion. Maxima have a characteristic density that diverges with the amplitude of phase variations and their formation is analogous to that of caustics in geometrical optics. We analyze in detail caustic formation in a quasi-one-dimensional condensate, which before expansion is subject to a periodic or random optical potential, and we discuss the equivalent problem for a quasi-two-dimensional system. We also examine the influence of many-body correlations in the initial state on caustic formation for a Bose gas expanding from a strictly one-dimensional trap. In addition, we study a similar arrangement for noninteracting fermions, showing that Fermi surface discontinuities in the momentum distribution give rise in that case to sharp peaks in the spatial derivative of the density. We discuss recent experiments and argue that fringes reported in time of flight images [Chen et al., Phys. Rev. A 77, 033632 (2008)] are an example of caustic formation.