Chemical Oscillation in Ultracold Chemistry

Physical Review A, 2001

We study the system of coupled atomic and molecular condensates within the two-mode model and beyond mean-field theory (MFT). Large amplitude atom-molecule coherent oscillations are shown to be damped by the rapid growth of fluctuations near the dynamically unstable molecular mode. This result contradicts earlier predictions about the recovery of atom-molecule oscillations in the two-mode limit. The frequency of the damped oscillation is also shown to scale as √ N / log N with the total number of atoms N , rather than the expected pure √ N scaling. Using a linearized model, we obtain analytical expressions for the initial depletion of the molecular condensate in the vicinity of the instability, and show that the important effect neglected by mean field theory is an initially non-exponential 'spontaneous' dissociation into the atomic vacuum. Starting with a small population in the atomic mode, the initial dissociation rate is sensitive to the exact atomic amplitudes, with the fastest (super-exponential) rate observed for the entangled state, formed by spontaneous dissociation.

arXiv (Cornell University), 2001

Physical Review Letters, 2012

Density-wave patterns in (quasi-) discrete media with local interactions are known to be unstable. We demonstrate that stable double-and triple-period patterns (DPPs and TPPs), with respect to the period of the underlying lattice, exist in media with nonlocal nonlinearity. This is shown in detail for dipolar Bose-Einstein condensates (BECs), loaded into a deep one-dimensional (1D) optical lattice (OL), by means of analytical and numerical methods in the tight-binding limit. The patterns featuring multiple periodicities are generated by the modulational instability of the continuous-wave (CW) state, whose period is identical to that of the OL. The DPP and TPP emerge via phase transitions of the second and first kind, respectively. The emerging patterns may be stable provided that the dipole-dipole (DD) interactions are repulsive and sufficiently strong, in comparison with the local repulsive nonlinearity. Within the set of the considered states, the TPPs realize a minimum of the free energy. Accordingly, a vast stability region for the TPPs is found in the parameter space, while the DPP stability region is relatively narrow. The same mechanism may create stable density-wave patterns in other physical media featuring nonlocal interactions, such as arrayed optical waveguides with thermal nonlinearity. PACS numbers: 03.75.Lm; 05.45.Yv

Physical Review A, 2006

We propose a scheme for making a Bose-Einstein condensate ͑BEC͒ of molecules from a BEC of atoms in a strongly confining two-dimensional optical lattice and a weak one-dimensional optical lattice in the third dimension. The stable solutions obtained for the order parameters take the form of a different type of gap soliton, with both atomic and molecular BECs, and also standard gap solitons with only a molecular BEC. The strongly confining dimensions of the lattice stabilize the BEC against inelastic energy transfer in atommolecule collisions. The solitons with atoms and molecules may be obtained by starting with an atomic BEC, and gradually tuning the resonance by changing the external magnetic-field strength until the desired atommolecule soliton is obtained. A gap soliton of a BEC of only molecules may be obtained nonadiabatically by starting from an atom-only gap soliton, far from a Feshbach resonance and adjusting the magnetic field to near Feshbach resonance. After a period of time in which the dimer field grows, change the magnetic field such that the detuning is large and negative and Feshbach effects wash out, turn off the optical lattice in phase with the atomic BEC, and turn on an optical lattice in phase with the molecules. The atoms disperse, leaving a gap soliton composed of a molecular BEC. Regarding instabilities in the dimension of the weak optical lattice, the solitons which are comprised of both atoms and molecules are sometimes stable and sometimes unstable-we present numerically obtained results. Gap solitons comprised of only molecules have the same stability properties as the standard gap solitons: stable from frequencies slightly below the middle of the band gap to the top, and unstable below that point. Instabilities are only weakly affected by the soliton velocities, and all instabilities are oscillatory.

Physical Review A, 2004

A dynamical many body theory of single color photoassociation in a Bose-Einstein condensate is presented. The theory describes the time evolution of a condensed atomic ensemble under the influence of an arbitrarily varying near resonant laser pulse, which strongly modifies the binary scattering properties. In particular, when considering situations with rapid variations and high light intensities the approach described in this article leads, in a consistent way, beyond standard mean field techniques. This allows to address the question of limits to the photoassociation rate due to many body effects which has caused extensive discussions in the recent past. Both, the possible loss rate of condensate atoms and the amount of stable ground state molecules achievable within a certain time are found to be stronger limited than according to mean field theory. By systematically treating the dynamics of the connected Green's function for pair correlations the resonantly driven population of the excited molecular state as well as scattering into the continuum of non-condensed atomic states are taken into account. A detailed analysis of the low energy stationary scattering properties of two atoms modified by the near resonant photoassociation laser, in particular of the dressed state spectrum of the relative motion prepares for the analysis of the many body dynamics. The consequences of the finite lifetime of the resonantly coupled bound state are discussed in the two body as well as in the many body context. Extending the two body description to scattering in a tight trap reveals the modifications to the near resonant adiabatic dressed levels caused by the decay of the excited molecular state.

arXiv: Quantum Gases, 2018

Exchange of energy by means of light-matter interaction provides a new dimension to various nonlinear dynamical systems. Here, the effects of light-matter interaction are investigated for a situation, where two counter-propagating, orthogonally polarized laser pulses are incident on the atomic condensate. It's observed that a localized laser pulse profile can induce localized modes in Bose-Einstein condensate. A stability analysis performed using Vakhitov-Kolokolov-like criterion has established that these localized modes are stable, when the atom-atom interaction is repulsive. The cooperative effects of light-matter interactions and atom-atom interactions on the Lieb-mode have been studied in the stable region through atomic dispersion, revealing the signature of bound state formation when the optical potential is Pöschl-Teller type. The energy diagram also indicates a continuous transfer of energy from the laser pulses to the atoms as the light-matter interaction changes its sign. PACS. 03.75.Lm Bose-Einstein condensates in periodic potentials-05.45.Yv SOlitons-32.80.Qk Coherent control of atomic interactions with photons

Fundamental World of Quantum Chemistry, 2003

The possibility, envisaged in 1925 by Einstein following the suggestion of Bose, of a dilute gas of atoms being condensed into a single quantum state was experimentally achieved in 1995 following decades of research. An avalanche of experiment and theory has followed, leading to the awarding of the 2001 Nobel Prizes in Physics to three of the pioneering experimentalists. Theory, mostly couched in the language and formalism of condensed matter physics, has developed apace. What we point out here is that a condensate in a double well trap may be thought of exactly as a diatomic molecule with delocalized molecular orbitals (MOs) filled with Bosons, rather than electrons. As in quantum chemistry, configuration interaction must be included to supplement the MO picture if dissociation is to be correctly described. Such dissociation is called condensate fragmentation in the condensed matter theory literature. Natural orbitals and their occupation numbers provide a clear and succinct way of determining "where the atoms are" in highly correlated states as fragmentation occurs, and are particularly helpful in understanding what is actually happening when energy levels with macroscopic occupancy "cross" as a function of breaking the symmetry between the trap wells. It is seen that only a few particles are actually active in the level crossing. Recent experiments in super-conductive Josephson loops showing tunneling of macroscopic quantum states are easily included in this picture.

Physical review letters, 2008

We discuss the dynamics of an atomic Bose-Einstein condensate when pairs of atoms are converted into molecules by single-color photoassociation. Three main regimes are found and it is shown that they can be understood on the basis of time-dependent two-body theory. In particular, the so-called rogue dissociation regime [Phys. Rev. Lett., 88, 090403 (2002)], which has a density-dependent limit on the photoassociation rate, is identified with a transient regime of the two-atom dynamics exhibiting universal properties. Finally, we illustrate how these regimes could be explored by photoassociating condensates of alkaline-earth atoms.

Arxiv preprint arXiv:0712.3672, 2007

The non-linear coupled Gross-Pitaevskii equation governing the dynamics of the two component Bose-Einstein condensate (TBEC) is shown to admit sinusoidal, propagating wave solutions in quasi one dimensional geometry in a trap. The solutions exist for a wide parameter range, which illustrates the procedure for coherent control of these modes through temporal modulation of the parameters, like scattering length and oscillator frequency. The effects of time dependent coupling and the trap variation on the condensate profile are explicated. The TBEC has also been investigated in presence of an optical lattice potential, where the superfluid phase is found to exist under general conditions.

Physical Review A, 2009

The non-linear coupled Gross-Pitaevskii equation governing the dynamics of the two component Bose-Einstein condensate (TBEC) is shown to admit sinusoidal, propagating wave solutions in quasi one dimensional geometry in a trap. The solutions exist for a wide parameter range, which illustrates the procedure for coherent control of these modes through temporal modulation of the parameters, like scattering length and oscillator frequency. The effects of time dependent coupling and the trap variation on the condensate profile are explicated. The TBEC has also been investigated in presence of an optical lattice potential, where the superfluid phase is found to exist under general conditions.