Sodium Bose-Einstein Condensate Research Articles

Seeded spin-mixing interferometry with long-time evolution in microwave-dressed sodium spinor Bose-Einstein condensates

We experimentally demonstrate a new type of spin-mixing interferometry in sodium Bose–Einstein condensates (BECs) based on seeded initial states. Seeding is useful because it speeds up the generation of entangled pairs, allowing many collisions to take place quickly, creating large populations in the arms of the interferometer. The entangled probe states of our interferometer are generated via spin-exchange collisions in F = 1 spinor BECs, where pairs of atoms with the magnetic quantum number collide and change into pairs with . Our results show that our seeded spin-mixing interferometer beats the standard quantum limit (SQL) with a metrological gain of 3.69 dB with spin-mixing time t = 10 ms in the case of single-sided seeding, and 3.33 dB with spin-mixing time t = 8 ms in the case of double sided seeding. The mechanism for beating the SQL is two-mode spin squeezing generated via spin-exchange collisions. Our results on spin-mixing interferometry with seeded states are useful for future quantum technologies such as quantum-enhanced microwave sensors, and quantum parametric amplifiers based on spin-mixing.

Mean-field spin-oscillation dynamics beyond the single-mode approximation for a harmonically trapped spin-1 Bose-Einstein condensate

Compared to single-component Bose-Einstein condensates, spinor Bose-Einstein condensates display much richer dynamics. In addition to density oscillations, spinor Bose-Einstein condensates exhibit intriguing spin dynamics that is associated with population transfer between different hyperfine components. This paper analyzes the validity of the widely employed single-mode approximation when describing the spin dynamics in response to a quench of the system Hamiltonian. The single-mode approximation assumes that the different hyperfine states all share the same time-independent spatial mode. This implies that the resulting spin Hamiltonian only depends on the spin interaction strength and not on the density interaction strength. Taking the spinor sodium Bose-Einstein condensate in the $f=1$ hyperfine manifold as an example and working within the mean-field theory framework, it is found numerically that the single-mode approximation misses, in some parameter regimes, intricate details of the spin and spatial dynamics. We develop a physical picture that explains the observed phenomenon. Moreover, using that the population oscillations described by the single-mode approximation enter into the effective potential felt by the mean-field spinor, we derive a semiquantitative condition for when dynamical mean-field induced corrections to the single-mode approximation are relevant. Our mean-field results have implications for a variety of published and planned experimental studies.

High-Performance Sodium Bose–Einstein Condensate Apparatus with a Hybrid Trap and Long-Distance Magnetic Transfer**Supported by the National Basic Research Program of China under Grant No 2013CB922002, and the National Natural Science Foundation of China under Grant No 11474347.

We report on the production of large sodium Bose–Einstein condensates in a hybrid of magnetic quadrupole and optical dipole trap. With an optimized spin-flip Zeeman slower, 2×1010 sodium atoms are captured in the magneto-optical trap (MOT). A long distance magnetic transfer setup moves the cold atom over 46 cm from the MOT chamber to the UHV science chamber, which provides great optical access and long conservative trap lifetime. After evaporative cooling in the hybrid trap, we produce nearly pure condensates of 1×107 atoms with lifetime of 80 s in the optical dipole trap.

Alternate Oscillation between Scissors and Quadrupole Modes in Sodium Bose–Einstein Condensates

Using an additional off-axis Helmholtz coil, we modulated the strength of a magnetic field at the center of a cloverleaf trap for sodium Bose–Einstein condensates so that it passed through zero for a few milliseconds. At a modulation time of 1 ms, a scissors mode and a high-lying quadrupole mode were generated independently, which had the same Landau damping rates of 39(10) 1/s. However, at 2 ms, alternate oscillation between the scissors mode and the high-lying quadrupole mode, whose frequency was twice that of the scissors mode, was observed with the frequency of the low-lying quadrupole mode.

Linearly aligned superradiant Bose-Einstein condensates diffracted by a single short laser pulse

Multiorder bidirectional superradiant Bose-Einstein condensates (BECs) were generated in a straight line by an irradiation of a single unidirectional short laser pulse along the long axis of a cigar-shaped sodium BEC in a magnetic trap. The probabilities of the diffracted BECs as a function of the laser intensity were well explained by the square of the Bessel functions and it was estimated that the intensity of the end-fire beam was 25$%$ of the laser intensity. The backward diffractions disappeared at pulse duration longer than 5 \ensuremath{\mu}s because of energy conservation. The probability for the $+$first-order diffraction grew exponentially with pulse duration when the backward diffractions disappeared. We observed the linearly aligned diffracted BECs along the propagation direction of the laser beam, regardless of the aspect ratio of the condensates. This fact indicates that the end-fire beam is triggered by the small backreflection from the vacuum window.

Collisional loss rates of sodium Bose-Einstein condensates in theF=2state in a one-dimensional optical lattice

We have created stable sodium Bose-Einstein condensates in the $|F=1,{m}_{F}=\ensuremath{-}1\ensuremath{\rangle}$ state in a one-dimensional optical lattice with a lifetime of 102 $\ifmmode\pm\else\textpm\fi{}$ 42 s, which is limited by the photon scattering rate. The condensates were transferred to the upper hyperfine $F$ $=$ 2 state and the one-body and two-body loss rates were examined. Condensates in the $|2,1\ensuremath{\rangle}$ state were transferred in the optical lattice from the initially prepared condensates using a two-photon microwave\char21{}radio-frequency pulse. The two-body loss coefficients in the $|2,0\ensuremath{\rangle}$ and $|2,1\ensuremath{\rangle}$ states were found to be (2.1 $\ifmmode\pm\else\textpm\fi{}$ 1.4) $\ifmmode\times\else\texttimes\fi{}$ 10${}^{\ensuremath{-}12}$ and (7.7 $\ifmmode\pm\else\textpm\fi{}$ 1.0) $\ifmmode\times\else\texttimes\fi{}$ 10${}^{\ensuremath{-}13}$ cm${}^{3}$ s${}^{\ensuremath{-}1}$, respectively. The lifetime of the $|2,1\ensuremath{\rangle}$ state was 15 ms at the initial density of 5 $\ifmmode\times\else\texttimes\fi{}$ 10${}^{14}$ atoms/cm${}^{3}$. We constructed a Ramsey atom interferometer using BECs in the $|1,\ensuremath{-}1\ensuremath{\rangle}$, and $|2,1\ensuremath{\rangle}$ states with an interrogation time of 2 ms in the optical lattice.

Quantum Phase Transition in an Antiferromagnetic Spinor Bose-Einstein Condensate

We have experimentally observed the dynamics of an antiferromagnetic sodium Bose-Einstein condensate quenched through a quantum phase transition. Using an off-resonant microwave field coupling the F = 1 and F = 2 atomic hyperfine levels, we rapidly switched the quadratic energy shift q from positive to negative values. At q = 0, the system undergoes a transition from a polar to antiferromagnetic phase. We measured the dynamical evolution of the population in the F = 1, mF = 0 state in the vicinity of this transition point and observed a mixed state of all 3 hyperfine components for q < 0. We also observed the coarsening dynamics of the instability for q < 0, as it nucleated small domains that grew to the axial size of the cloud.

Optimized evaporative cooling for sodium Bose-Einstein condensation against three-body loss

We report on a highly efficient evaporative cooling optimized experimentally. We successfully created sodium Bose-Einstein condensates with 6.4\ifmmode\times\else\texttimes\fi{}10${}^{7}$ atoms starting from 6.6\ifmmode\times\else\texttimes\fi{}10${}^{9}$ thermal atoms trapped in a magnetic trap by employing a fast linear sweep of radio frequency at the final stage of evaporative cooling so as to overcome the serious three-body losses. The experimental results such as the cooling trajectory and the condensate growth quantitatively agree with the numerical simulations of evaporative cooling on the basis of the kinetic theory of a Bose gas carefully taking into account our specific experimental conditions. We further discuss theoretically a possibility of producing large condensates, more than 10${}^{8}$ sodium atoms, by simply increasing the number of initial thermal trapped atoms and the corresponding optimization of evaporative cooling.

Production of sodium Bose–Einstein condensates in an optical dimple trap

We report on the realization of a sodium Bose–Einstein condensate (BEC) in a combined red-detuned optical dipole trap formed by two beams crossing in a horizontal plane and a third, tightly focused dimple trap (dT) propagating vertically. We produce a BEC in three main steps: loading of the crossed dipole trap from laser-cooled atoms, an intermediate evaporative cooling stage that results in efficient loading of the auxiliary dT, and a final evaporative cooling stage in the dT. Our protocol is implemented in a compact setup and allows us to reach quantum degeneracy even with relatively modest initial atom numbers and available laser power.

Ramsey Spectroscopy and Geometric Operations on Sodium Bose–Einstein Condensates Using Two-Photon Stimulated Raman Transitions

Ramsey spectroscopy and geometric operations on the released sodium Bose–Einstein condensates consisting of 10 7 atoms were demonstrated using copropagating two-photon stimulated Raman pulses, which were resonant to the clock transition between the F =1, m F =0 and F =2, m F =0 states of sodium atoms. The Ramsey fringes with a visibility close to 1 were obtained for two Raman pulses separated by 10 ms. A relative frequency resolution of Ramsey resonance was 6×10 -10 and a phase uncertainty of fringes was 0.06 rad for single measurement. Using resonant laser-controlled Raman pulses, geometric operations for rotations of the two-level Bose–Einstein condensates around axes 2 and 3 on the Bloch sphere were also demonstrated with a relative phase uncertainty of 4%.

All-optical generation and photoassociative probing of sodium Bose–Einstein condensates

We demonstrate an all-optical technique to evaporatively produce sodium Bose–Einstein condensates (BEC). We use a crossed-dipole trap formed from light near 1 μm, and a simple ramp of the intensity to force evaporation. In addition, we introduce photoassociation as diagnostic of the trap loading process, and show that it can be used to detect the onset of BEC. Finally, we demonstrate the straightforward production of multiple traps with condensates using this technique, and that some control over the spinor state of the BEC is achieved by positioning the trap as well.

Bragg spectroscopy of vortex lattices in Bose-Einstein condensates

We have measured the velocity field of a vortex lattice within a sodium Bose-Einstein condensate using Bragg scattering. The phase gradient of the macroscopic wavefunction was mapped into the spatial structure of the diffracted atom cloud, allowing for single shot measurement of the rotation parameters. A combination of spectral and spatial information yields a complete description of the superfluid flow, coarse-grained over the lattice structure, including direct and independent measurements of the rate and sense of rotation. Signatures of the microscopic quantum rotation have also been observed.

Optically plugged quadrupole trap for Bose-Einstein condensates

We created sodium Bose-Einstein condensates in an optically plugged quadrupole magnetic trap (OPT). A focused, 532nm laser beam repelled atoms from the coil center where Majorana loss is significant. We produced condensates of up to $3 \times 10^7$ atoms, a factor of 60 improvement over previous work [1], a number comparable to the best all-magnetic traps, and transferred up to $9 \times 10^6$ atoms into a purely optical trap. Due to the tight axial confinement and azimuthal symmetry of the quadrupole coils, the OPT shows promise for creating Bose-Einstein condensates in a ring geometry.

Analysis of dynamical tunneling experiments with a Bose-Einstein condensate

Dynamical tunnelling is a quantum phenomenon where a classically forbidden process occurs, that is prohibited not by energy but by another constant of motion. The phenomenon of dynamical tunnelling has been recently observed in a sodium Bose-Einstein condensate. We present a detailed analysis of these experiments using numerical solutions of the three dimensional Gross-Pitaevskii equation and the corresponding Floquet theory. We explore the parameter dependency of the tunnelling oscillations and we move the quantum system towards the classical limit in the experimentally accessible regime.

Inelastic time-dependent tunnelling of matter waves

Tunnelling of ultra-cold atoms across a periodically displaced optical barrier exhibits characteristic inelastic effects as well as remarkable transparency at energies for which the same barrier, if stationary, would be opaque. Such phenomena could be observed with sodium Bose-Einstein condensate wavepackets and could be exploited for atom-laser sideband generation.

Useful models of four-wave mixing in Bose–Einstein condensates

A recent experiment demonstrated four-wave mixing of wavepackets in a sodiumBose–Einstein condensate (Deng et al 1999 Nature 398 218). This was followed by atheoretical and numerical treatment of the experiment (Trippenbach et al 2000 Phys. Rev.A 62 02368). In the experiment, a short period of free expansion of the condensate, afterrelease from the magnetic trap, was followed by a set of two Bragg pulses which createdmoving wavepackets. These wavepackets, due to nonlinear interaction and underphase-matching conditions, created a new momentum component in a four-wave mixingprocess. We propose simple mathematical models for this process. Next we suggest that,instead of exactly matching the frequencies as in the abovementioned experiments,we introduce a small mismatch in the energies, and therefore the frequenciesΔω.We show that such a small mismatch can compensate for the initial phases that are builton the condensate during free expansion. A physical explanation is offered. Thiscompensation can improve the efficiency of four-wave mixing; in some cases even increasingit by a factor of 2. We also deal with the situation where two strong wavepackets areaccompanied by a weak input beam applied as a seed both with and without a mismatch.Here the influence of the mismatch is less obviously beneficial. We also comment onrecent work by Ketterle’s group (Vogels et al 2002 Phys. Rev. Lett. 89 020401).

Enhancement of four-wave mixing in Bose-Einstein condensate by introducing a mismatch

A recent experiment demonstrated four-wave mixing of wave packets in a sodium Bose-Einstein condensate [Deng et al., Nature (London) 398, 218 (1999)]. This was followed by a theoretical and numerical treatment of the experiment [Trippenbach et al., Phys. Rev. A 62, 023608 (2000)]. In the experiment, a short time of free expansion of the condensate, after it was released from the magnetic trap, was followed by a set of two Bragg pulses, which created moving wave packets. These wave packets, due to nonlinear interaction and under phase-matching conditions created a new momentum component in a four-wave mixing process. Here we suggest that, instead of exactly matching the frequencies as in the above-mentioned experiments, we admit a small mismatch in energies, and therefore frequencies $\ensuremath{\Delta}\ensuremath{\omega}.$ We show that such a small mismatch can compensate for the initial phases built on the condensate during free expansion. A physical explanation is offered. This compensation can be beneficial for the efficiency of the four-wave mixing, in some cases even increasing it by a factor of 2.

Sodium Bose-Einstein condensates in the F = 2 state in a large-volume optical trap.

We have investigated the properties of Bose-Einstein condensates of sodium atoms in the upper hyperfine ground state. Condensates in the high-field seeking [F=2, m(F)=-2> state were created in a large volume optical trap from initially prepared [F=1, m(F)=-1> condensates using a microwave transition at 1.77 GHz. We found condensates in the stretched state [F=2, m(F)=-2> to be stable for several seconds at densities in the range of 10(14) atoms/cm(3). In addition, we studied the clock transition [F=1, m(F)=0> --> [F=2, m(F)=0> in a sodium Bose-Einstein condensate and determined a density-dependent frequency shift of (2.44+/-0.25+/-0.5) x 10(-12) Hz cm(3).

Bragg spectroscopy and superradiant Rayleigh scattering in a Bose–Einstein condensate

Two sets of studies concerning the interaction of off-resonant light with a sodium Bose–Einstein condensate are described. In the first set, properties of a Bose–Einstein condensate were studied using Bragg spectroscopy. The high momentum and energy resolution of this method allowed a spectroscopic measurement of the mean-field energy and of the intrinsic momentum distribution of the condensate. Depending on the momentum transfer, both the phonon regime as well as the free-particle regime could be explored. In the second set of studies, the cigar-shaped condensate was exposed to a single off-resonant laser beam and highly directional scattering of light and atoms was observed. This collective light scattering was caused by the long coherence time of the quasi-particles in the condensate and resulted in a new form of matter wave amplification.

Diffraction of a Released Bose-Einstein Condensate by a Pulsed Standing Light Wave

We study the diffraction of a released sodium Bose-Einstein condensate by a pulsed standing light wave. The width of the momentum distribution of the diffracted atoms exhibits strong oscillations as a function of the pulse duration, corresponding to periodic focusing and collimation of the condensate inside the standing light wave. Applications of this thick grating regime of diffraction to atom interferometry are discussed.