Rubidium Bose-Einstein Condensate Research Articles

Rapid generation and number-resolved detection of spinor rubidium Bose-Einstein condensates

High data acquisition rates and low-noise detection of ultracold neutral atoms present important challenges for the state tomography and interferometric application of entangled quantum states in Bose-Einstein condensates. In this article, we present a high-flux source of $^{87}$Rb Bose-Einstein condensates combined with a number-resolving detection. We create Bose-Einstein condensates of $2\times10^5$ atoms with no discernible thermal fraction within $3.3$ s using a hybrid evaporation approach in a magnetic/optical trap. For the high-fidelity tomography of many-body quantum states in the spin degree of freedom [arXiv:2207.01270], it is desirable to select a single mode for a number-resolving detection. We demonstrate the low-noise selection of subsamples of up to $16$ atoms and their subsequent detection with a counting noise below $0.2$ atoms. The presented techniques offer an exciting path towards the creation and analysis of mesoscopic quantum states with unprecedented fidelities, and their exploitation for fundamental and metrological applications.

The Influence of s-Wave Interactions on Focussing of Atoms

The focusing of a rubidium Bose–Einstein condensate via an optical lattice potential is numerically investigated. The results are compared with a classical trajectory model which underestimates the width of the focused beam. Via the inclusion of the effects of interactions into the classical trajectories model, we show that it is possible to obtain reliable estimates for the width of the focused beam when compared to numerical integration of the Gross–Pitaevskii equation. Finally, we investigate the optimal regimes for focusing and find that for a strongly interacting Bose–Einstein condensate focusing of order 20 nm may be possible.

Optical focusing of Bose-Einstein condensates

We theoretically investigate the optical focusing of a rubidium Bose-Einstein condensate onto a planar surface. Our analysis uses a Gaussian variational method that includes the effects of two-body atom-atom interactions and three-body recombination losses. The essential factors such as the width, peak density and atom loss rate of the focused BEC profile on the surface are investigated and compared to Gross-Pitaevskii numerical simulations. We find a reasonable agreement in the results between our analytical approach and the numerical simulations. Our analysis predicts that condensates of $10^5$ atoms could be focused down to $\sim 10$nm widths, potentially allowing nanometer-scale atomic deposition with peak densities greater than $10^5$ atoms/$\mu$m$^2$.

Rabi oscillations and Ramsey-type pulses in ultracold bosons: Role of interactions

Double-well systems loaded with one, two, or many quantum particles give rise to intriguing dynamics, ranging from Josephson oscillation to self-trapping. This work presents theoretical and experimental results for two distinct double-well systems, both created using dilute rubidium Bose-Einstein condensates with particular emphasis placed on the role of interaction in the systems. The first is realized by creating an effective two-level system through Raman coupling of hyperfine states. The second is an effective two-level system in momentum space generated through the coupling by an optical lattice. Even though the non-interacting systems can, for a wide parameter range, be described by the same model Hamiltonian, the dynamics for these two realizations differ in the presence of interactions. The difference is attributed to scattering diagrams that contribute in the lattice coupled system but vanish in the Raman coupled system. The internal dynamics of the Bose-Einstein condensates for both coupling scenarios is probed through a Ramsey-type interference pulse sequence, which constitutes a key building block of atom interferometers. These results have important implications in a variety of contexts including lattice calibration experiments and momentum space lattices used for quantum analog simulations.

Observation of Bose-Einstein condensates in an Earth-orbiting research lab.

Quantum mechanics governs the microscopic world, where low mass and momentum reveal a natural wave-particle duality. Magnifying quantum behaviour to macroscopic scales is a major strength of the technique of cooling and trapping atomic gases, in which low momentum is engineered through extremely low temperatures. Advances in this field have achieved such precise control over atomic systems that gravity, often negligible when considering individual atoms, has emerged as a substantial obstacle. In particular, although weaker trapping fields would allow access to lower temperatures1,2, gravity empties atom traps that are too weak. Additionally, inertial sensors based on cold atoms could reach better sensitivities if the free-fall time of the atoms after release from the trap could be made longer3. Planetary orbit, specifically the condition of perpetual free-fall, offers to lift cold-atom studies beyond such terrestrial limitations. Here we report production of rubidium Bose-Einstein condensates (BECs) in an Earth-orbiting research laboratory, the Cold Atom Lab. We observe subnanokelvin BECs in weak trapping potentials with free-expansion times extending beyond one second, providing an initial demonstration of the advantages offered by a microgravity environment for cold-atom experiments and verifying the successful operation of this facility. With routine BEC production, continuing operations will support long-term investigations of trap topologies unique to microgravity4,5, atom-laser sources6, few-body physics7,8 and pathfinding techniques for atom-wave interferometry9-12.

Experimental Investigation of the Electromagnetically Induced-Absorption-Like Effect for an N-Type Energy Level in a Rubidium BEC**Supported by the National Key Research and Development Program of China under Grant No 2016YFA0301602, the National Natural Science Foundation of China under Grant Nos 11474188 and 11704234, the Fund for Shanxi ‘1331 Project’ Key Subjects Construction, and the Program of Youth Sanjin Scholar.

We study the electromagnetically induced-absorption-like (EIA-like) effect for an n-type system in an 87Rb Bose–Einstein condensate (BEC) using the absorption imaging technique for coupling and driving lasers operating at the D1 and D2 lines of 87Rb. The coherent effect is probed by measuring the number of atoms remaining after the BEC is exposed to strong driving fields and a weak probe field. The absorption imaging technique accurately reveals the EIA-like effect of the n-type system. This coherent effect in an n-type system is useful for optical storage, tunable optical switching, and so on.

Spontaneous spin squeezing in a rubidium BEC

We describe an experiment where spin squeezing occurs spontaneously within a standard Ramsey sequence driving a two-component Bose–Einstein condensate (BEC) of 87Rb atoms trapped in an elongated magnetic trap. The squeezing is generated by state-dependent collisional interactions, despite the near-identical scattering lengths of the spin states in 87Rb. In our proof-of-principle experiment, we observe a metrological spin squeezing that reaches 1.3 ± 0.4 dB for 5000 atoms, with a contrast of 90 ± 1%. The method may be applied to realize spin-squeezed BEC sources for atom interferometry without the need for cavities, state-dependent potentials or Feshbach resonances.

Going beyond the first Chern number

Quantum Simulation Topological properties of physical systems are reflected in so-called Chern numbers: A nonzero Chern number typically means that a system is topologically nontrivial. Sugawa et al. engineered a cold atom system with a nonzero second Chern number, in contrast to condensed matter physics, where only the first Chern number is usually invoked. The exotic topology relates to the emergence of a type of magnetic monopole called the Yang monopole (known from theoretical high-energy physics) in a five-dimensional space of internal degrees of freedom in a rubidium Bose-Einstein condensate. The results illustrate the potential of cold atoms physics to simulate high-energy phenomena. Science , this issue p. [1429][1] [1]: /lookup/doi/10.1126/science.aam9031

Fast production of rubidium Bose–Einstein condensate in a dimple trap

We reported a simple scheme of producing Bose–Einstein condensate (BEC) in a dimple trap. Starting from a regular magneto-optical trap (MOT), we apply a temporal dark MOT to increase the atom density and directly load atoms into a crossed dipole trap. In order to make the trap frequency relatively high at the end of evaporation, a tight dimple is added. Such a scheme ensures relatively high trap volume for loading atoms and high trap frequency for evaporative cooling. The BEC phase transition is observed after 12 s evaporation. Furthermore, we demonstrated the manipulation of the hyperfine states with a Raman coupling, which is very useful for studying many-body physics via Ramsey or spin-echo spectroscopy.

Production of Rubidium Bose—Einstein Condensate in an Optically Plugged Magnetic Quadrupole Trap**Supported by the National Natural Science Foundation of China under Grant Nos 11434015, 91336106 and 11004224, and the National Basic Research Program of China under Grant No 2011CB921601.

We experimentally produce the rubidium Bose—Einstein condensate in an optically plugged magnetic quadrupole trap. A far blue-detuned focused laser beam with a wavelength of 532 nm is plugged in the center of the magnetic quadrupole trap to increase the number of trapped atoms and to suppress the heating. An rf evaporative cooling in the magneto-optical hybrid trap is applied to decrease the atom temperature into degeneracy. The atom number of the condensate is 1.2(0.4) × 105 and the temperature is below 100 nK. We also study characteristic behaviors of the condensate, such as phase space density, condensate fraction and anisotropic expansion.

Optimizing quantum gas production by an evolutionary algorithm

We report on the application of an evolutionary algorithm (EA) to enhance performance of an ultra-cold quantum gas experiment. The production of a $^{87}$Rubidium Bose-Einstein condensate (BEC) can be divided into fundamental cooling steps, specifically magneto optical trapping of cold atoms, loading of atoms to a far detuned crossed dipole trap and finally the process of evaporative cooling. The EA is applied separately for each of these steps with a particular definition for the feedback the so-called fitness. We discuss the principles of an EA and implement an enhancement called differential evolution. Analyzing the reasons for the EA to improve \eg, the atomic loading rates and increase the BEC phase-space density, yields an optimal parameter set for the BEC production and enables us to reduce the BEC production time significantly. Furthermore, we focus on how additional information about the experiment and optimization possibilities can be extracted and how the correlations revealed allow for further improvement. Our results illustrate that EAs are powerful optimization tools for complex experiments and exemplify that the application yields useful information on the dependence of these experiments on the optimized parameters.

Precision measurement of theRb87tune-out wavelength in the hyperfine ground stateF=1at 790 nm

We report on a precision measurement of the $D$ line tune-out wavelength of $^{87}$Rubidium in the hyperfine ground state $|F=1, m_F=0,\pm1 \rangle$ manifold at 790 nm, where the scalar ac Stark shifts of the $D_1$ and the $D_2$ lines cancel. This wavelength is sensitive to usually neglected contributions from vector and tensor ac Stark shifts, transitions to higher principle quantum numbers, and core electrons. The ac Stark shift is probed by Kapitza-Dirac scattering of a Rubidium Bose-Einstein condensate in a one-dimensional optical lattice in free space and controlled magnetic environment. The tune-out wavelength of the magnetically insensitive $m_F=0$ state was determined to 790.01858(23) nm with sub pm accuracy. An in situ absolute polarization, and magnetic background field measurement is performed by employing the ac vector Stark shift for the $m_F=\pm 1$ states. Comparing our findings to theory, we get quantitative insight into atomic physics beyond commonly used two-level atom approximations or the neglect of inner shell contributions.

Optimal preparation of quantum states on an atom-chip device

Atom chips provide compact and robust platforms towards practical quantum technologies. A quick and faithful preparation of arbitrary input states for these systems is crucial but represents a very challenging experimental task. This is especially difficult when the dynamical evolution is noisy and unavoidable setup imperfections have to be considered. Here, we experimentally prepare with very high small errors different internal states of a Rubidium Bose-Einstein condensate realized on an atom chip. As a possible application of our scheme, we apply it to improve the sensitivity of an atomic interferometer.

Nonlinear dressed states at the miscibility-immiscibility threshold

The dynamical evolution of spatial patterns in a complex system can reveal the underlying structure and stability of stationary states. As a model system we employ a two-component rubidium Bose-Einstein condensate at the transition from miscible to immiscible with the additional control of linear interconversion. Excellent agreement is found between the detailed experimental time evolution and the corresponding numerical mean-field computations. Analyzing the dynamics of the system, we find clear indications of stationary states that we term nonlinear dressed states. A steady state bifurcation analysis reveals a smooth connection of these states with dark-bright soliton solutions of the integrable two-component Manakov model.

Landau damping and frequency-shift of a quadrupole mode in a disc-shaped rubidium Bose—Einstein condensate

The damping and frequency-shift in Landau mechanism of a quadrupole mode in a disc-shaped rubidium Bose—Einstein condensate are investigated by using the Hartree—Fock—Bogoliubov approximation. The practical relaxations of the elementary excitations and the orthometric relation among them are taken into account to obtain advisable calculation formula for damping as well as frequency-shift. The first approximation of Gaussian distribution function is employed for the ground-state wavefunction to suitably eliminate the divergence of the analytic three-mode coupling matrix elements. According to these methods, both Landau damping rate and frequency-shift of the quadrupole mode are analytically calculated. In addition, all the theoretical results agree with the experimental ones.

Experimental realization of quantum zeno dynamics

It is generally impossible to probe a quantum system without disturbing it. However, it is possible to exploit the back action of quantum measurements and strong couplings to tailor and protect the coherent evolution of a quantum system. This is a profound and counterintuitive phenomenon known as quantum Zeno dynamics. Here we demonstrate quantum Zeno dynamics with a rubidium Bose–Einstein condensate in a five-level Hilbert space. We harness measurements and strong couplings to dynamically disconnect different groups of quantum states and constrain the atoms to coherently evolve inside a two-level subregion. In parallel to the foundational importance due to the realization of a dynamical superselection rule and the theory of quantum measurements, this is an important step forward in protecting and controlling quantum dynamics and, broadly speaking, quantum information processing.

Development of narrow linewidth, micro-integrated extended cavity diode lasers for quantum optics experiments in space

We present a micro-integrated extended cavity diode laser module for experiments on rubidium Bose–Einstein condensates and atom interferometry at 780.24 nm onboard a sounding rocket. The micro-integration concept is optimized for space application. The laser chip, micro-lenses, a volume holographic Bragg grating, micro-temperature sensors and a micro-thermoelectric cooler are integrated on an aluminium nitride ceramic micro-optical bench with a foot print of only 50 × 10 mm2. Moveable parts are omitted to allow for a very compact and robust design. The laser module provides an output power of more than 120 mW at a short term (170 μs) linewidth of 54 kHz, both full-width-at-half-maximum. The laser can be coarsely tuned by 44 GHz with a continuous tuning range of 31 GHz. The micro-integration technology presented here can be transferred to other wavelengths.

Stability of nonstationary states of spin-2 Bose-Einstein condensates

The dynamical stability of nonstationary states of homogeneous spin-2 rubidium Bose-Einstein condensates is studied. The states considered are such that the spin vector remains parallel to the magnetic field throughout the time evolution, making it possible to study the stability analytically. These states are shown to be stable in the absence of an external magnetic field, but they become unstable when a finite magnetic field is introduced. It is found that the growth rate and wavelength of the instabilities can be controlled by tuning the strength of the magnetic field and the size of the condensate.

Testing the equivalence between the canonical and Minkowski momentum of light with ultracold atoms

We design an experimental system to test the equivalence between the canonical and Minkowski momentum of light, which can provide a judgment on the recent resolution of the century-old Abraham-Minkowski controversy by S. M. Barnett [Phys. Rev. Lett. 104, 070401 (2010)]. By measuring the recoil momentum of ultracold rubidium atoms in a rubidium Bose-Einstein condensate after the electromagnetically induced absorption of a monochromatic laser pulse, the momentum of the pulse in the ultracold atoms can be obtained. If the equivalence is valid, the measured results will coincide with the theoretical values of the canonical momentum of the pulse. Otherwise, if the equivalence is invalid, the measured results will coincide with the theoretical values of the Minkowski momentum, which are significantly different from that of the canonical momentum. Our scheme is amethod to test the equivalence between the canonical and Minkowski momentum of light. It can also be improved to distinguish between the Minkowski and Abraham momenta to contribute to the study of the Abraham-Minkowski controversy in the future.

A synthetic electric force acting on neutral atoms

Electromagnetism is a simple example of a gauge theory where the underlying potentials -- the vector and scalar potentials -- are defined only up to a gauge choice. The vector potential generates magnetic fields through its spatial variation and electric fields through its time-dependence. We experimentally produce a synthetic gauge field that emerges only at low energy in a rubidium Bose-Einstein condensate: the neutral atoms behave as charged particles do in the presence of a homogeneous effective vector potential. We have generated a synthetic electric field through the time dependence of an effective vector potential, a physical consequence even though the vector potential is spatially uniform.