One-dimensional Optical Potential Research Articles

Resonant enhancement of the Fulde-Ferell-Larkin-Ovchinnikov state in three dimensions by a one-dimensional optical potential

We describe an imbalanced superfluid Fermi gas in three dimensions within the path-integral framework. To allow for the formation of the Fulde-Ferell-Larkin-Ovchinnikov state (FFLO state), a suitable form of the saddle point is chosen, in which the pairs have a finite center-of-mass momentum. To test the correctness of this path-integral description, the zero-temperature phase diagram for an imbalanced Fermi gas in three dimensions is calculated, and compared to recent theoretical results. Subsequently, we investigate two models that describe the effect of imposing a one-dimensional (1D) optical potential on the three-dimensional (3D) imbalanced Fermi gas. We show that this 1D optical potential can greatly enlarge the stability region of the FFLO state, relative to the case of the 3D Fermi gas without 1D periodic modulation. Furthermore, it is shown that there exists a direct connection between the center-of-mass momentum of the FFLO pairs and the wave vector of the optical potential. We propose that this concept can be used experimentally to resonantly enhance the stability region of the FFLO state.

Imbalanced Fermi superfluid in a one-dimensional optical potential

The superfluid properties of a two-state Fermi mixture in an optical lattice are profoundly modified when an imbalance in the population of the two states is present. We present analytical solutions for the free energy and for the gap and number equations in the saddle-point approximation describing resonant superfluidity in the quasi-two-dimensional gas. Inhomogeneities due to the trapping potentials can be taken into account using the local-density approximation. Analyzing the free energy in this approximation, we find that phase separation occurs in the layers. The phase diagram of the superfluid and normal phases is derived, and analytical expressions for the phase lines are presented. We complete the investigation by accounting for effects beyond mean field in the Bose-Einstein condensate limit, where the system is more properly described as a Bose-Fermi mixture of atoms and molecules.

Loading Bose-Einstein-condensed atoms into the ground state of an optical lattice

We optimize the turning on of a one-dimensional optical potential, ${V}_{L}(x,t)=S(t){V}_{0}\phantom{\rule{0.2em}{0ex}}{\mathrm{cos}}^{2}(kx)$ to obtain the optimal turn-on function $S(t)$ so as to load a Bose-Einstein condensate into the ground state of the optical lattice of depth ${V}_{0}$. Specifically, we minimize interband excitations at the end of the turn-on of the optical potential at the final ramp time ${t}_{r}$, where $S({t}_{r})=1$, given that $S(0)=0$. Detailed numerical calculations confirm that a simple unit cell model is an excellent approximation when the turn-on time ${t}_{r}$ is long compared with the inverse of the band excitation frequency and short in comparison with nonlinear time $\ensuremath{\hbar}∕\ensuremath{\mu}$ where $\ensuremath{\mu}$ is the chemical potential of the condensate. We demonstrate using the Gross-Pitaevskii equation with an optimal turn-on function $S(t)$ that the ground state of the optical lattice can be loaded with no significant excitation even for times ${t}_{r}$ on the order of the inverse band excitation frequency.

All-Optical Constant-Force Laser Tweezers

Optical tweezers are a powerful tool for the study of single biomolecules. Many applications require that a molecule be held under constant tension while its extension is measured. We present two schemes based on scanning-line optical tweezers to accomplish this, providing all-optical alternatives to force-clamp traps that rely on electronic feedback to maintain constant-force conditions for the molecule. In these schemes, a laser beam is rapidly scanned along a line in the focal plane of the microscope objective, effectively creating an extended one-dimensional optical potential over distances of up to 8 μm. A position-independent lateral force acting on a trapped particle is created by either modulating the laser beam intensity during the scan or by using an asymmetric beam profile in the back focal plane of the microscope objective. With these techniques, forces of up to 2.69 pN have been applied over distances of up to 3.4 μm with residual spring constants of <26.6 fN/ μm. We used these techniques in conjunction with a fast position measurement scheme to study the relaxation of λ-DNA molecules against a constant external force with submillisecond time resolution. We compare the results to predictions from the wormlike chain model.

Motion of laser-cooled atoms in an optical potential.

The motion of laser-cooled $^{85}\mathrm{Rb}$ atoms along a one-dimensional optical potential under the influence of an external force is investigated. The transition from a region of low external force, where the motion is dominated by the optical potential, to one of a strong force, where the presence of the optical potential is hardly felt, is demonstrated. An unexpected discrepancy is found between the measured and expected value of the drift velocity induced by an applied magnetic field on a one-dimensional ${\mathrm{\ensuremath{\sigma}}}^{+}$-${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}}$ optical molasses.