Precise control of quantum particles is required for many interesting or novel experiments. Here we consider the task of transporting an atom using an external harmonic potential from one well of an optical lattice to another without motional excitations. To achieve this we apply techniques from Shortcuts to Adiabaticity (STA) enabling fast and robust state manipulation. The process is split up into three independent building blocks; first the atom is loaded into an additional external harmonic trap; this trap is then transported from one lattice site to another and finally the atom is unloaded back onto the lattice by opening the external harmonic trap. We design protocols for each of these building blocks separately using invariant-based inverse engineering. Additionally we extend this method to the transport of a Bose-Einstein condensate described by the Gross-Pitaevskii equation.
We investigate the fast transport of an atom or a packet of atoms by different kinds of non-harmonic traps including power-law traps. The study is based on the reverse engineering method. Exact results are obtained and applied to design robust transport protocols. The optimization of the transport trajectory is performed with classical trajectories, and remains valid for the transport of a wave packet.
Exactly solvable model of two Rydberg-dressed atoms moving in a quasi-two-dimensional harmonic trap is introduced and its properties are investigated. Depending on the strength of inter-particle interactions and the critical range of the potential, the two-particle eigenstates are classified with respect to the excitations of the center-of-mass motion, relative angular momentum, and relative distance variable. Having these solutions in hand, we discuss inter-particle correlations as functions of interaction parameters. We also present a straightforward prescription of how to generalize obtaine…
Employing a short-range two-channel description we derive an analytic model of atoms in isotropic and anisotropic harmonic traps at a Feshbach resonance. On this basis we obtain a new parameterization of the energy-dependent scattering length which differs from the one previously employed. We validate the model by comparison to full numerical calculations for Li-Rb and explain quantitatively the experimental observation of a resonance shift and trap-induced molecules in exited bands. Finally, we analyze the bound state admixture and Landau-Zener transition probabilities.
We consider controlled collisions between two ultracold atoms guided by external harmonic potentials. We derive analytical solutions of the Schroedinger equation for this system, and investigate the properties of eigenergies and eigenstates for different trap geometries as a function of a trap separation and of the scattering length. When varying the trap separation the energy spectrum exhibits avoided crossings, corresponding to trap-induced shape resonances. Introducing an energy-dependent scattering length we investigate the behavior of the system in the vicinity of a magnetic Feshbach reso…
We apply the Schrödinger factorization to construct the ladder operators for hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator in arbitrary dimensions. By generalizing these operators we show that the dynamical algebra for these problems is the $su(1,1)$ Lie algebra.
We consider optical high harmonic generation in a hydrogen atom confined in a breathing spherical box by considering atomic nucleus as fixed at the center of sphere. In such spherically symmetric, dynamical trap, the high harmonic generation spectrum is calculated at different values of the oscillation amplitude, confinement size and atomic nucleus charge.
Two identical dipolar atoms moving in a harmonic trap without an external magnetic field are investigated. Using the algebra of angular momentum a semi - analytical solutions are found. We show that the internal spin - spin interactions between the atoms couple to the orbital angular momentum causing an analogue of Einstein - de Haas effect. We show a possibility of adiabatically pumping our system from the s-wave to the d-wave relative motion. The effective spin-orbit coupling occurs at anti-crossings of the energy levels.
We propose a simplest detector of harmonic vibrations with micro amplitudes and low frequencies, i.e. the detector consisting of one atomic beam. Here the atomic beam is induced by a plane harmonic wave and has a classical collective harmonic vibrations, which vibrant directions are perpendicular to the wave vectors of atomic beam. Compared with the detector consisting of atomic Mach-Zehnder interferometer, the new detector has two advantages: (1) it is suitable for the detection of the harmonic vibrations induced either by a longitudinal plane harmonic wave or by a transverse plane harmonic w…
We here explore Majorana Fermion states in an s-wave superfluid of cold atoms in the presence of spin-orbital coupling and an additional harmonic potential. The superfluid boundary is induced by a harmonic trap. Two locally separated Majorana Fermion states are revealed numerically based on the self-consistent Bogoliubov-de Gennes equations. The local density of states are calculated, through which the signatures of Majorana excitations may be indicated experimentally.
The Kravchuk and Meixner polynomials of discrete variable are introduced for the discrete models of the harmonic oscillator and hydrogen atom. Starting from Rodrigues formula we construct raising and lowering operators, commutation and anticommutation relations. The physical properties of discrete models are figured out through the equivalence with the continuous models obtained by limit process.
We study the entanglement dynamics of the two two-level atoms coupling with a single-mode polarized cavity field after incorporating the atomic centers of mass classical harmonic vibrations with micro amplitudes and low frequencies. We propose a quantitative vibrant factor to modify the concurrence of the two atoms states. When the vibrant frequencies are very low, we obtain that: (i) the factor depends on the relative vibrant displacements and the initial phases rather than the absolute amplitudes, and reduces the concurrence to three orders of magnitude; (ii) the concurrence increases with t…
Self-organization effects related to light amplification in the collective atomic recoil laser system with the driven atoms confined in a harmonic trap are investigated further. In the dispersive parametric region, our study reveals that the spontaneously formed structures in the phase space contributes an important role to the light amplification of the probe field under the atomic motion being modified by the trap.
We consider the system of two interacting atoms confined in axially symmetric harmonic trap. Within the pseudopotential approximation, we solve the Schroedinger equation exactly, discussing the limits of quasi-one and quasi-two-dimensional geometries. Finally, we discuss the application of an energy-dependent pseudopotential, which allows to extend the validity of our results to the case of tight traps and large scattering lengths.
A method is proposed to cool down atoms in a harmonic trap without phase-space compression as in a perfectly slow adiabatic expansion, i.e., keeping the populations of the instantaneous initial and final levels invariant, but in a much shorter time. This may require that the harmonic trap becomes an expulsive parabolic potential in some time interval. The cooling times achieved are also shorter than previous minimal times using optimal-control bang-bang methods and real frequencies.
We investigate a single laser driven atom trapped in a non-harmonic potential. We present the performance of ground-state laser cooling and Doppler cooling and the signatures of the center-of-mass motion in the power spectrum of the scattered light. In order to illustrate the results we provide two explicit examples for the confining potential: the infinite square well and the Morse potential.
We consider optical harmonic generation in time-dependent box driven by external time-periodic field. Two types of the external field is considered: Time-periodic optical field and a field created by harmonically oscillating wall of the box. The latter is treated on in terms of the Schrodinger equation with time-dependent boundary conditions.
We have studied the atomic density of a cloud confined in an isotropic harmonic trap at the vicinity of the Bose-Einstein transition temperature. We show that, for a non-interacting gas and near this temperature, the ground-state density has the same order of magnitude as the excited states density at the centre of the trap. This holds in a range of temperatures where the ground-state population is negligible compared to the total atom number. We compare the exact calculations, available in a harmonic trap, to semi-classical approximations. We show that these latter should include the ground-s…
The quantum dynamics of an atom with a magnetic quadrupole moment that interacts with an external field subject to a harmonic and a linear confining potentials is investigated. It is shown that the interaction between the magnetic quadrupole moment and an electric field gives rise to an analogue of the Coulomb potential and, by confining this atom to a harmonic and a linear confining potentials, a quantum effect characterized by the dependence of the angular frequency on the quantum numbers of the system is obtained. In particular, it is shown that the possible values of the angular frequency …
We study the absorption spectrum for a strongly degenerate Fermi gas confined in a harmonic trap. The spectrum is calculated using both the exact summation and also the Thomas-Fermi (TF) approximation. In the latter case, relatively simple analytical expressions are obtained for the absorption lineshape at large number of trapped atoms. At zero temperature, the approximated lineshape is characterized by a $(1-z^2)^{5/2}$ dependence which agrees well with the exact numerical calculations. At non-zero temperature, the spectrum becomes broader, although remains non-Gaussian as long as the fermion…
Rotation of atoms in a lattice is studied using a Hubbard model. It is found that the atoms are still contained in the trap even when the rotation frequency is larger than the trapping frequency. This is very different from the behavior in continuum. Bragg scattering and coupling between angular and radial motion are believed to make this stability possible. In this regime, density depletion at the center of the trap can be developed for spin polarized fermions.
We report on a highly efficient waveguide resonator device for the production of 775 nm light using a titanium indiffused LiNbO3waveguide resonator. When scanning the resonance the device produces up to 110 mW of second harmonic power with 140 mW incident on the device - an external conversion efficiency of 75 %. The cavity length is also locked, using a Pound-Drever-Hall type locking scheme, involving feedback to either the cavity temperature or the laser frequency. With laser frequency feedback a stable output power of approximately 28 mW from a 52 mW pump is seen over one hour.
We study the population inversion and Q-function of a two-level atom, interacting with single-mode laser light field, in a $q$-analog harmonic oscillator trap for increasing $q$. For $τ=.003(q=e^τ)$ the collapses and revivals of population inversion become well defined facilitating experimental observation but for large $τ\sim 0.1$ the time dependence of population inversion is completely wiped out.
We analyze the dynamics of two atoms with a short-ranged pair interaction in a one-dimensional harmonic trap with time-dependent frequency. Our analysis is focused on two representative cases: (i) a sudden change of the trapping frequency from one value to another, and (ii) a periodic trapping frequency. In case (i), the dynamics of the interacting and the corresponding non-interacting systems turn out to be similar. In the second case, however, the interacting system can behave quite differently, especially close to parametric resonance. For instance, in the regions where such resonance occur…
We investigate quantum entanglement between two (spin-1/2) fermions inside a cylindrical harmonic trap, making use of the von Neumann entropy for the reduced single particle density matrix as the pure state entanglement measure. We explore the dependence of pair entanglement on the geometry and strength of the trap and on the strength of the pairing interaction over the complete range of the effective BCS to BEC crossover. Our result elucidates an interesting connection between our model system of two fermions and that of two interacting bosons.
In this article we formulate frictionless atom cooling in harmonic traps as a time-optimal control problem, permitting imaginary values of the trap frequency for trasient time intervals during which the trap becomes an expulsive parabolic potential. We show that the minimum time solution has "bang-bang" form, where the frequency jumps suddenly at certain instants and then remains constant, and calculate estimates of the minimum cooling time for various numbers of such jumps. A numerical optimization method based on pseudospectral approximations is used to obtain suboptimal realistic solutions …
We theoretically investigate the properties of two interacting ultracold highly magnetic atoms trapped in a one-dimensional harmonic potential. The atoms interact via an anisotropic long-range dipole-dipole interaction, which in one dimension effectively can be modeled by the contact interaction. We investigate the interplay of the external magnetic field, the spin-spin interaction, and the trapping potential and how they affect the magnetization of the system. We show the role of indistinguishability and symmetries in the dynamics by studying the time evolution of the observables that could b…
In this paper we consider a quantum harmonic oscillator interacting with the electromagnetic radiation field in the presence of a boundary condition preserving the continuous spectrum of the field, such as an infinite perfectly conducting plate. Using an appropriate Bogoliubov-type transformation we can diagonalize exactly the Hamiltonian of our system in the continuum limit and obtain non-perturbative expressions for its ground-state energy. From the expressions found, the atom-wall Casimir-Polder interaction energy can be obtained, and well-know lowest-order results are recovered as a limiti…
A single superconducting artificial atom provides a unique basis for coupling electromagnetic fields and photons hardly achieved with a natural atom. Bringing a pair of harmonic oscillators into resonance with transitions of the three-level atom converts atomic spontaneous processes into correlated emission dynamics. We demonstrate two-mode correlated emission lasing on harmonic oscillators coupled via the fully controllable three-level artificial atom. Correlation of two different color emissions reveals itself as equally narrowed linewiths and quench of their mutual phase-diffusion. The mutu…
Under certain conditions, the quantum delta-kicked harmonic oscillator displays quantum resonances. We consider an atom-optical realization of the delta-kicked harmonic oscillator, and present a theoretical discussion of the quantum resonances that could be observed in such a system. Having outlined our model of the physical system we derive the values at which quantum resonances occur and relate these to potential experimental parameters. We discuss the observable effects of the quantum resonances, using the results of numerical simulations. We develop a physical explanation for the quantum r…
The classical Hamiltonian system of time-dependent harmonic oscillator driven by the arbitrary external time-dependent force is considered. Exact analytical solution of the corresponding equations of motion is constructed in the framework of the technique (Robnik M, Romanovski V G, J. Phys. A: Math. Gen. {\bf 33} (2000) 5093) based on WKB approach. Energy evolution for the ensemble of uniformly distributed w.r.t. the canonical angle initial conditions on the initial invariant torus is studied. Exact expressions for the energy moments of arbitrary order taken at arbitrary time moment are analyt…
We investigate the effect of dynamic electron correlation on high-harmonic generation in helium atoms using intense visible light (λ=390nm). Two complementary approaches are used which account for correlation in an approximate manner: time-dependent density-functional theory and a single-active-electron model. For intensities I~10^{14} W/cm^2, the theories are in remarkably good agreement for the dynamic polarization and harmonic spectrum. This is attributed to a low-frequency collective mode together with a high-frequency single-electron response due to the nuclear singularity, both of which …
As a serious attempt for constructing a new foundation for describing micro-entities from a causal standpoint, it was explained before in [1, 2, 3] that by unifying the concepts of information, matter and energy, each micro-entity is assumed to be composed of a probability field joined to a particle called a particle-field or PF system. The relativistic generalization of this theory and its invariance under Lorentz transformation has been proved. In this essay, based on the relativistic generalization of Schrodinger equation derived in [4], we solve the relativistic Schrodinger equation for re…
A harmonic oscillator model in four dimensions is presented for the helium atom to estimate the distance to the inner and outer electron from the nucleus, the angle between electrons and the energy levels. The method is algebraic and is not based on the choice of correct trial wave function. Three harmonic oscillators and thus three quantum numbers are sufficient to describe the two-electron system. We derive a simple formula for the energy in the general case and in the special case of the Wannier Ridge. For a set of quantum numbers the distance to the electrons and the angle between the elec…
The problem of the Kohn mode in bosonized theories of one-dimensional interacting fermions in the harmonic trap is investigated and a suitable modification of the interaction is proposed which preserves the Kohn mode. The modified theory is used to calculate exactly the inhomogeneous linear mobility at position z in response to a spatial force pulse at another position. It is found the inhomogeneous particle mobility exhibits resonances not only at the trap frequency but also at multiples of a new renormalized collective mode frequency which depends on the strength of the interaction. In contr…
High-order harmonic generation (HHG) by hydrogenlike atoms/ions in the uniform periodic electric field, formed by the two linearly polarized counterpropagating laser beams of relativistic intensities, is studied. The relativistic quantum theory of HHG in such fields, at which the impeding factor of relativistic magnetic drift of a strong wave can be eliminated, is presented arising from the Dirac equation. Specifically, a scheme of HHG in underdense plasma with the copropagating ultraintense laser and fast ion beams is proposed.
Bang-bang control is often used to implement a minimal-time shortcut to adiabaticity for efficient transport of atoms in a moving harmonic trap. However, drastic changes of the on-off controller, leading to high transport-mode excitation and energy consumption, become infeasible under realistic experimental conditions. To circumvent these problems, we propose smooth bang-bang protocols with near-minimal time, by setting the physical constraints on the relative displacement, speed, and acceleration between the mass center of the atom and the trap center. We adopt Pontryagin's maximum principle …
We suggest that atoms undergoing Bragg deflection from a cavity field introduce entanglement between their external degrees of freedom. The atoms interact with an electromagnetic cavity field which is far detuned from atomic transition frequency and is in superposition state. We provide a set of experimental parameters in order to perform the suggested experiment within the frame work of the presently available technology.
Spectroscopic labels for a few particles with spin that are harmonically trapped in one-dimension with effectively zero-range interactions are provided by quantum numbers that characterize the symmetries of the Hamiltonian: permutations of identical particles, parity inversion, and the separability of the center-of-mass. The exact solutions for the non-interacting and infinitely repulsive cases are reduced with respect to these symmetries. This reduction explains how states of single-component and multi-component fermions and bosons transform under adiabatic evolution from non-interacting to s…
We analize the dipole spectrum of a two-level atom excited by a non-resonant intense monochromatic field, under the electric dipole approximation and beyond the rotating wave approximation. We show that the apparently complex spectral structure can be completely described by two families: harmonic frequencies of the driving field and field-induced nonlinear fluorescence. Our formulation of the problem provides quantitative laws for the most relevant spectral features: harmonic ratios and phases, non-perturbative Stark shift, and frequency limits of the harmonic plateau. In particular, we demon…
We describe the collisional interaction between two different atoms that are trapped in a harmonic potential. The atoms are exposed to a magnetic field, which is modulated in the vicinity of an s-wave Feshbach resonance, and we study the formation of molecular bound states and excited states of the trapped system with non-trivial angular correlations.
Frictionless atom cooling in harmonic traps is formulated as a time-optimal control problem and a synthesis of optimal controlled trajectories is obtained. This work has already been used to determine the minimum time for transition between two thermal states and to show the emergence of the third law of classical thermodynamics from quantum thermodynamics. It can also find application in the fast adiabatic-like expansion of Bose-Einstein condensates, with possible applications in atom interferometry. This paper is based on our recently published article in SIAM J. Control Optim.
Phase-Sensitive Heterodyne Detection of MW using EIT Harmonics in Rydberg Atoms
Johns Hopkins University（约翰斯·霍普金斯大学）；Indian Institute of Science（印度科学学院）；Defence Institute of Advanced Technology (Deemed University)（国防先进技术研究所（认定大学））；University of Bristol（布里斯托大学）；Indian Institute of Technology Guwahati（印度理工学院古瓦哈提分校）
Gaussian state decoherence aspects due to interacting magnetic-like and gravitational fields are quantified through the quantum fidelity and Shannon entropy in the scope of the phase-space representation of elementary quantum systems. For Gaussian Wigner functions describing harmonic oscillator states, an interacting external field destroys the quantum fidelity and introduces a quantum beating behavior. Likewise, it introduces harmonic profiles for free particle systems. Some aspects of quantum decoherence for the quantum harmonic oscillator and for the free particle limit are also quantified …
Using an asymptotic phase representation of the particle density operator $\hatρ(z)$ in the one-dimensional harmonic trap, the part $δ\hatρ_F(z)$ which describes the Friedel oscillations is extracted. The expectation value $<δ\hatρ_F(z)>$ with respect to the interacting ground state requires the calculation of the mean square average of a properly defined phase operator. This calculation is performed analytically for the Tomonaga-Luttinger model with harmonic confinement. It is found that the envelope of the Friedel oscillations at zero temperature decays with the boundary exponent $ν= (K+1)/2…
We study the splitting of a harmonically trapped atomic Bose-Einstein condensate when we continuously turn up an optical lattice (or a double-well) potential. As the lattice height is increased, quantum fluctuations of atoms are enhanced. The resulting nonequilibrium dynamics of the fragmentation process of the condensate, the loss of the phase coherence of atoms along the lattice, and the reduced atom number fluctuations in individual lattice sites are stochastically studied within the truncated Wigner approximation. We perform a detailed study of the effects of temperature and lattice height…
We present some theoretical results on the lattice vibrations that are necessary for a concise derivation of the Debye-Waller factor in the harmonic approximation. First we obtain an expression for displacement of an atom in a crystal lattice from its equilibrium position. Then we show that an atomic displacement has the Gaussian distribution. Finally, we obtain the computational formula for the Debye-Waller factor in the Debye model.
