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Spinor Bose–Einstein condensates

Spinor Bose gases form a family of quantum fluids manifesting both magnetic order and superfluidity. This article reviews experimental and theoretical progress in understanding the static and dynamic properties of these fluids. The connection between system properties and the rotational symmetry properties of the atomic states and their interactions are investigated. Following a review of the experimental techniques used for characterizing spinor gases, their mean-field and many-body ground states, both in isolation and under the application of symmetry-breaking external fields, are discussed. These states serve as the starting point for understanding low-energy dynamics, spin textures and topological defects, effects of magnetic dipole interactions, and various non-equilibrium collective spin-mixing phenomena. The paper aims to form connections and establish coherence among the vast range of works on spinor Bose gases, so as to point to open questions and future research opportunities.

Spinor Bose gases: Symmetries, magnetism, and quantum dynamics

The technique of stimulated Raman adiabatic passage (STIRAP), which allows efficient and selective population transfer between quantum states without suffering loss due to spontaneous emission, was introduced in 1990 (Gaubatz \emph{et al.}, J. Chem. Phys. \textbf{92}, 5363, 1990). Since then STIRAP has emerged as an enabling methodology with widespread successful applications in many fields of physics, chemistry and beyond. This article reviews the many applications of STIRAP emphasizing the developments since 2000, the time when the last major review on the topic was written (Vitanov \emph{et al.}, Adv. At. Mol. Opt. Phys. \textbf{46}, 55, 2001). A brief introduction into the theory of STIRAP and the early applications for population transfer within three-level systems is followed by the discussion of several extensions to multi-level systems, including multistate chains and tripod systems. The main emphasis is on the wide range of applications in atomic and molecular physics (including atom optics, cavity quantum electrodynamics, formation of ultracold molecules, precision experiments, etc.), quantum information (including single- and two-qubit gates, entangled-state preparation, etc.), solid-state physics (including processes in doped crystals, nitrogen-vacancy centers, superconducting circuits, etc.), and even some applications in classical physics (including waveguide optics, frequency conversion, polarization optics, etc.). Promising new prospects for STIRAP are also presented (including processes in optomechanics, detection of parity violation in molecules, spectroscopy of core-nonpenetrating Rydberg states, and population transfer with X-ray pulses).

Stimulated Raman adiabatic passage in physics, chemistry, and beyond

Determination of the gravitational constant G using laser-cooled atoms and quantum interferometry, a technique that gives new insight into the systematic errors that have proved elusive in previous experiments, yields a value that has a relative uncertainty of 150 parts per million and which differs from the current recommended value by 1.5 combined standard deviations. The Newtonian gravitational constant G, also known as the universal gravitational constant or 'big G', is a fundamental physical constant that is used in the calculation of gravitational attraction between two bodies. There are several ways to measure G with high precision, but these measurements disagree, presumably because of the intervention of unknown errors in the different experiments. With the aim of identifying and ultimately removing the systematic errors that give rise to these discrepancies, Gabriele Rosi and colleagues have carried out a high-precision measurement of G using quantum interferometry with laser-cooled atoms, an experimental approach that differs radically from previous determinations. The authors obtain a value for G with a precision of ∼0.015% — approaching that of the traditional measurements, and with prospects for considerable further improvement. Although this result doesn't yet solve the problem of the discrepant measurements, the use of such a radically different technique holds promise for identifying the systematic errors that have plagued previous determinations. About 300 experiments have tried to determine the value of the Newtonian gravitational constant, G, so far, but large discrepancies in the results have made it impossible to know its value precisely1. The weakness of the gravitational interaction and the impossibility of shielding the effects of gravity make it very difficult to measure G while keeping systematic effects under control. Most previous experiments performed were based on the torsion pendulum or torsion balance scheme as in the experiment by Cavendish2 in 1798, and in all cases macroscopic masses were used. Here we report the precise determination of G using laser-cooled atoms and quantum interferometry. We obtain the value G = 6.67191(99) × 10−11 m3 kg−1 s−2 with a relative uncertainty of 150 parts per million (the combined standard uncertainty is given in parentheses). Our value differs by 1.5 combined standard deviations from the current recommended value of the Committee on Data for Science and Technology3. A conceptually different experiment such as ours helps to identify the systematic errors that have proved elusive in previous experiments, thus improving the confidence in the value of G. There is no definitive relationship between G and the other fundamental constants, and there is no theoretical prediction for its value, against which to test experimental results. Improving the precision with which we know G has not only a pure metrological interest, but is also important because of the key role that G has in theories of gravitation, cosmology, particle physics and astrophysics and in geophysical models.

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Precision measurement of the Newtonian gravitational constant using cold atoms

We report on Bose-Einstein condensation in a gas of strontium atoms, using laser cooling as the only cooling mechanism. The condensate is formed within a sample that is continuously Doppler cooled to below $1\text{ }\text{ }\ensuremath{\mu}\mathrm{K}$ on a narrow-linewidth transition. The critical phase-space density for condensation is reached in a central region of the sample, in which atoms are rendered transparent for laser cooling photons. The density in this region is enhanced by an additional dipole trap potential. Thermal equilibrium between the gas in this central region and the surrounding laser cooled part of the cloud is established by elastic collisions. Condensates of up to ${10}^{5}$ atoms can be repeatedly formed on a time scale of 100 ms, with prospects for the generation of a continuous atom laser.

Laser cooling to quantum degeneracy.

We report on the realization of quantum degenerate gas mixtures of the alkaline-earth-metal element strontium with the alkali-metal element rubidium. A key ingredient of our scheme is sympathetic cooling of Rb by Sr atoms that are continuously laser cooled on a narrow-linewidth transition. This versatile technique allows us to produce ultracold gas mixtures with a phase-space density of up to 0.06 for both elements. By further evaporative cooling we create double Bose-Einstein condensates of ${}^{87}$Rb with either ${}^{88}$Sr or ${}^{84}$Sr, reaching more than $1\ifmmode\times\else\texttimes\fi{}{10}^{5}$ condensed atoms per element for the ${}^{84}$Sr-${}^{87}$Rb mixture. These quantum gas mixtures constitute an important step towards the production of a quantum gas of polar, open-shell RbSr molecules.

Quantum degenerate mixtures of strontium and rubidium atoms

We report on the creation of ultracold $^{84}\mathrm{Sr}_{2}$ molecules in the electronic ground state. The molecules are formed from atom pairs on sites of an optical lattice using stimulated Raman adiabatic passage (STIRAP). We achieve a transfer efficiency of 30% and obtain $4\ifmmode\times\else\texttimes\fi{}{10}^{4}$ molecules with full control over the external and internal quantum state. STIRAP is performed near the narrow $^{1}S_{0}\mathrm{\text{\ensuremath{-}}}^{3}P_{1}$ intercombination transition, using a vibrational level of the $1({0}_{u}^{+})$ potential as an intermediate state. In preparation of our molecule association scheme, we have determined the binding energies of the last vibrational levels of the $1({0}_{u}^{+})$, $1({1}_{u})$ excited-state and the $X\text{ }^{1}\ensuremath{\Sigma}_{g}^{+}$ ground-state potentials. Our work overcomes the previous limitation of STIRAP schemes to systems with magnetic Feshbach resonances, thereby establishing a route that is applicable to many systems beyond alkali-metal dimers.

Creation of Ultracold Sr 2 Molecules in the Electronic Ground State

We study the spinor properties of $S=3$ $^{52}\mathrm{Cr}$ condensates, in which dipole-dipole interactions allow changes in magnetization We observe a demagnetization of the Bose-Einstein condensate (BEC) when the magnetic field is quenched below a critical value corresponding to a phase transition between a ferromagnetic and a nonpolarized ground state, which occurs when spin-dependent contact interactions overwhelm the linear Zeeman effect The critical field is increased when the density is raised by loading the BEC in a deep 2D optical lattice The magnetization dynamics is set by dipole-dipole interactions

Spontaneous demagnetization of a dipolar spinor Bose gas in an ultralow magnetic field.

Magnetic Feshbach resonances allow control of the interactions between ultracold atoms1. They are an invaluable tool in studies of few-body and many-body physics2,3, and can be used to convert pairs of atoms into molecules4,5 by ramping an applied magnetic field across a resonance. Molecules formed from pairs of alkali atoms have been transferred to low-lying states, producing dipolar quantum gases6. There is great interest in making molecules formed from an alkali atom and a closed-shell atom such as ground-state Sr or Yb. Such molecules have both a strong electric dipole and an electron spin; they will open up new possibilities for designing quantum many-body systems7,8, and for tests of fundamental symmetries9. The crucial first step is to observe Feshbach resonances in the corresponding atomic mixtures. Very narrow resonances have been predicted theoretically10,11,12, but until now have eluded observation. Here we present the observation of magnetic Feshbach resonances of this type, for an alkali atom, Rb, interacting with ground-state Sr. Magnetically tunable scattering resonances between strontium and rubidium atoms are observed in an ultracold experiment, opening the door to exploring quantum many-body physics with new designed molecules.

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Benjamin Pasquiou

Papers

Laser cooling to quantum degeneracy.

Quantum degenerate mixtures of strontium and rubidium atoms

Creation of Ultracold Sr 2 Molecules in the Electronic Ground State

Spontaneous demagnetization of a dipolar spinor Bose gas in an ultralow magnetic field.

Observation of Feshbach resonances between alkali and closed-shell atoms