Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor
14 Jul 1995-Science (American Association for the Advancement of Science)-Vol. 269, Iss: 5221, pp 198-201
TL;DR: A Bose-Einstein condensate was produced in a vapor of rubidium-87 atoms that was confined by magnetic fields and evaporatively cooled and exhibited a nonthermal, anisotropic velocity distribution expected of the minimum-energy quantum state of the magnetic trap in contrast to the isotropic, thermal velocity distribution observed in the broad uncondensed fraction.
Abstract: A Bose-Einstein condensate was produced in a vapor of rubidium-87 atoms that was confined by magnetic fields and evaporatively cooled. The condensate fraction first appeared near a temperature of 170 nanokelvin and a number density of 2.5 x 10 12 per cubic centimeter and could be preserved for more than 15 seconds. Three primary signatures of Bose-Einstein condensation were seen. (i) On top of a broad thermal velocity distribution, a narrow peak appeared that was centered at zero velocity. (ii) The fraction of the atoms that were in this low-velocity peak increased abruptly as the sample temperature was lowered. (iii) The peak exhibited a nonthermal, anisotropic velocity distribution expected of the minimum-energy quantum state of the magnetic trap in contrast to the isotropic, thermal velocity distribution observed in the broad uncondensed fraction.
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TL;DR: A quantum state was designed and produced by optically imprinting a phase pattern onto a BEC of sodium atoms, and matter-wave interferometry with spatially resolved imaging was used to analyze the resultant phase distribution.
Abstract: Quantum phase engineering is demonstrated with two techniques that allow the spatial phase distribution of a Bose-Einstein condensate (BEC) to be written and read out. A quantum state was designed and produced by optically imprinting a phase pattern onto a BEC of sodium atoms, and matter-wave interferometry with spatially resolved imaging was used to analyze the resultant phase distribution. An appropriate phase imprint created solitons, the first experimental realization of this nonlinear phenomenon in a BEC. The subsequent evolution of these excitations was investigated both experimentally and theoretically.
999 citations
TL;DR: In this paper, the authors discuss the orbital angular momentum of light, outlines the theoretical basis for the orbital momentum of beams within the paraxial approximation, and indicates the unapproximated theory, based on the full set of Maxwell equations.
Abstract: Publisher Summary This chapter discusses the orbital angular momentum of light, outlines the theoretical basis for the orbital angular momentum of beams within the paraxial approximation, and indicates the unapproximated theory, based on the full set of Maxwell equations. The chapter discusses the problems associated with the separation and identification of spin and orbital contributions to the angular momentum properties of a field, the properties of Laguerre–Gaussian beams, which are physically realizable in the laboratory, and the ways in which the beams may be generated. It reviews the phenomenological behavior of beams possessing orbital angular momentum and their interaction with matter in bulk. The chapter also describes the measurement of the rotational Doppler shift, which arises when beams possessing orbital and spin angular momenta are rotated. The dipole-interaction of atoms with the orbital angular momentum of light beams is considered. The roles of spin and orbital angular momentum are also compared and contrasted.
994 citations
TL;DR: Interference of atomic de Broglie waves tunneling from a vertical array of macroscopically populated traps has been observed, closely related to the ac Josephson effect observed in superconducting electronic systems.
Abstract: Interference of atomic de Broglie waves tunneling from a vertical array of macroscopically populated traps has been observed. The traps were located in the antinodes of an optical standing wave and were loaded from a Bose-Einstein condensate. Tunneling was induced by acceleration due to gravity, and interference was observed as a train of falling pulses of atoms. In the limit of weak atomic interactions, the pulse frequency is determined by the gravitational potential energy difference between adjacent potential wells. The effect is closely related to the ac Josephson effect observed in superconducting electronic systems.
965 citations
TL;DR: Different realized and proposed techniques for creating gauge potentials-both Abelian and non-Abelian-in atomic systems and their implication in the context of quantum simulation are reviewed.
Abstract: Gauge fields are central in our modern understanding of physics at all scales. At the highest energy scales known, the microscopic universe is governed by particles interacting with each other through the exchange of gauge bosons. At the largest length scales, our Universe is ruled by gravity, whose gauge structure suggests the existence of a particle—the graviton—that mediates the gravitational force. At the mesoscopic scale, solid-state systems are subjected to gauge fields of different nature: materials can be immersed in external electromagnetic fields, but they can also feature emerging gauge fields in their low-energy description. In this review, we focus on another kind of gauge field: those engineered in systems of ultracold neutral atoms. In these setups, atoms are suitably coupled to laser fields that generate effective gauge potentials in their description. Neutral atoms ‘feeling’ laser-induced gauge potentials can potentially mimic the behavior of an electron gas subjected to a magnetic field, but also, the interaction of elementary particles with non-Abelian gauge fields. Here, we review different realized and proposed techniques for creating gauge potentials—both Abelian and non-Abelian—in atomic systems and discuss their implication in the context of quantum simulation. While most of these setups concern the realization of background and classical gauge potentials, we conclude with more exotic proposals where these synthetic fields might be made dynamical, in view of simulating interacting gauge theories with cold atoms.
960 citations
TL;DR: In this paper, the Bogoliubov equation is applied to the formation of a Bose-Einstein condensate in a box and in a harmonic trap, along with the dynamics of small-amplitude perturbations.
Abstract: After reviewing the ideal Bose-Einstein gas in a box and in a harmonic trap, the effect of interactions on the formation of a Bose-Einstein condensate are discussed, along with the dynamics of small-amplitude perturbations (the Bogoliubov equations). When the condensate rotates with angular velocity $\ensuremath{\Omega}$, one or several vortices nucleate, leading to many observable consequences. With more rapid rotation, the vortices form a dense triangular array, and the collective behavior of these vortices has additional experimental implications. For $\ensuremath{\Omega}$ near the radial trap frequency ${\ensuremath{\omega}}_{\ensuremath{\perp}}$, the lowest-Landau-level approximation becomes applicable, providing a simple picture of such rapidly rotating condensates. Eventually, as $\ensuremath{\Omega}\ensuremath{\rightarrow}{\ensuremath{\omega}}_{\ensuremath{\perp}}$, the rotating dilute gas is expected to undergo a quantum phase transition from a superfluid to various highly correlated (nonsuperfluid) states analogous to those familiar from the fractional quantum Hall effect for electrons in a strong perpendicular magnetic field.
929 citations
References
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Proceedings Article•
14 Jul 1996TL;DR: The striking signature of Bose condensation was the sudden appearance of a bimodal velocity distribution below the critical temperature of ~2µK.
Abstract: Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.
3,530 citations
TL;DR: The confinement and cooling of an optically dense cloud of neutral sodium atoms by radiation pressure was reported, provided by three retroreflected laser beams propagating along orthogonal axes, with a weak magnetic field used to distinguish between the beams.
Abstract: We report the confinement and cooling of an optically dense cloud of neutral sodium atoms by radiation pressure. The trapping and damping forces were provided by three retroreflected laser beams propagating along orthogonal axes, with a weak magnetic field used to distinguish between the beams. We have trapped as many as ${10}^{7}$ atoms for 2 min at densities exceeding ${10}^{11}$ atoms ${\mathrm{cm}}^{\ensuremath{-}3}$. The trap was \ensuremath{\simeq}0.4 K deep and the atoms, once trapped, were cooled to less than a millikelvin and compacted into a region less than 0.5 mm in diameter.
1,402 citations
TL;DR: In this article, the authors describe how the Phasenraum eines Lichtquants in bezug auf ein gegebenes Volumen wird in „Zellen“ von der Grose h3 aufgeteilt, i.e., the Zahl der moglichen Verteilungen der Lichtquanten einer makroskopisch definierten Strahlung unter diese Zellen liefert die Entropie.
Abstract: Der Phasenraum eines Lichtquants in bezug auf ein gegebenes Volumen wird in „Zellen“ von der Grose h3 aufgeteilt. Die Zahl der moglichen Verteilungen der Lichtquanten einer makroskopisch definierten Strahlung unter diese Zellen liefert die Entropie und damit alle thermodynamischen Eigenschaften der Strahlung.
1,329 citations
11 Jul 1988
TL;DR: This "Doppler cooling limit" results from the minimization of the detuning-dependent temperature at low laser power1.
Abstract: The generally accepted theory of laser cooling of free atoms predicts that the lowest achievable temperature is given by kaT = hγ/2, where kB is Boltzmann's constant arid γ is the natural linewidth of the transition for laser cooling. This "Doppler cooling limit" results from the minimization of the detuning-dependent temperature at low laser power1:
610 citations
"Observation of Bose-Einstein Conden..." refers background in this paper
...Of the three or four most prominent players in the development of laser cooling, two (David Wineland and Bill Phillips) are long-standing Bureau scientists; two of their most influential papers are described in this volume [6,7]....
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TL;DR: In this paper, an output coupler for Bose condensed atoms in a magnetic trap was demonstrated, where short pulses of rf radiation were used to create Bose condensates in a superposition of trapped and untrapped hyperfine states.
Abstract: We have demonstrated an output coupler for Bose condensed atoms in a magnetic trap. Short pulses of rf radiation were used to create Bose condensates in a superposition of trapped and untrapped hyperfine states. The fraction of out-coupled atoms was adjusted between 0% and 100% by varying the amplitude of the rf radiation. This configuration produces output pulses of coherent atoms and can be regarded as a pulsed ``atom laser.''
608 citations
"Observation of Bose-Einstein Conden..." refers background in this paper
...BEC is the starting point for this rapidly evolving technology— after atoms are cooled into a BEC, they are ejected out of the trap in a highly collimated, monoenergetic beam [16, 17]....
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