Brian P Anderson
 Associate Dean, Graduate Academic Affairs
 Professor, Optical Sciences
 Associate Professor, Physics
 Member of the Graduate Faculty
Contact
 (520) 6265825
 Meinel Optical Sciences, Rm. 632
 Tucson, AZ 85721
 bpanders@arizona.edu
Awards
 Fellow
 American Physical Society, Spring 2014
 American Physical Society, Spring 2013
Interests
No activities entered.
Courses
202425 Courses

Atom Optics
OPTI 549 (Spring 2025) 
Directed Graduate Research
OPTI 792 (Fall 2024) 
Dissertation
OPTI 920 (Fall 2024) 
Quantum Mechanics
OPTI 570 (Fall 2024)
202324 Courses

Atom Optics
OPTI 549 (Spring 2024) 
Directed Graduate Research
OPTI 792 (Spring 2024) 
Independent Study
OPTI 599 (Spring 2024) 
Master's Report
OPTI 909 (Spring 2024) 
Research
OPTI 900 (Spring 2024) 
Dissertation
OPTI 920 (Fall 2023) 
Quantum Mechanics
OPTI 570 (Fall 2023)
202223 Courses

Dissertation
OPTI 920 (Spring 2023) 
Independent Study
OPTI 599 (Spring 2023) 
Thesis
OPTI 910 (Spring 2023) 
Dissertation
OPTI 920 (Fall 2022) 
Independent Study
OPTI 599 (Fall 2022) 
Quantum Mechanics
OPTI 570 (Fall 2022) 
Research
OPTI 900 (Fall 2022) 
Thesis
OPTI 910 (Fall 2022)
202122 Courses

Dissertation
OPTI 920 (Spring 2022) 
Thesis
OPTI 910 (Spring 2022) 
Dissertation
OPTI 920 (Fall 2021) 
Quantum Mechanics
OPTI 570 (Fall 2021)
202021 Courses

Dissertation
OPTI 920 (Spring 2021) 
Independent Study
PHYS 399 (Spring 2021) 
Research
OPTI 900 (Spring 2021) 
Dissertation
OPTI 920 (Fall 2020) 
Independent Study
PHYS 399 (Fall 2020) 
Optical Physics Comp Lab
OPTI 571L (Fall 2020) 
Quantum Mechanics
OPTI 570 (Fall 2020) 
Research
OPTI 900 (Fall 2020)
201920 Courses

Dissertation
OPTI 920 (Spring 2020) 
Independent Study
PHYS 299 (Spring 2020) 
Quantum Mechanics
OPTI 345 (Spring 2020) 
Dissertation
OPTI 920 (Fall 2019) 
Independent Study
OPTI 599 (Fall 2019) 
Independent Study
PHYS 299 (Fall 2019) 
Optical Physics Comp Lab
OPTI 571L (Fall 2019) 
Quantum Mechanics
OPTI 570 (Fall 2019)
201819 Courses

Atom Optics
OPTI 549 (Spring 2019) 
Dissertation
OPTI 920 (Spring 2019) 
Independent Study
OPTI 599 (Spring 2019) 
Independent Study
PHYS 199 (Spring 2019) 
Dissertation
OPTI 920 (Fall 2018) 
Optical Physics Comp Lab
OPTI 571L (Fall 2018) 
Quantum Mechanics
OPTI 570 (Fall 2018)
201718 Courses

Dissertation
OPTI 920 (Spring 2018) 
Dissertation
OPTI 920 (Fall 2017) 
Optical Physics Comp Lab
OPTI 571L (Fall 2017) 
Quantum Mechanics
OPTI 570 (Fall 2017)
201617 Courses

Atom Optics
OPTI 549 (Spring 2017) 
Dissertation
OPTI 920 (Spring 2017) 
Directed Graduate Research
OPTI 792 (Fall 2016) 
Dissertation
OPTI 920 (Fall 2016) 
Independent Study
OPTI 599 (Fall 2016) 
Optical Physics Comp Lab
OPTI 571L (Fall 2016) 
Quantum Mechanics
OPTI 570 (Fall 2016)
201516 Courses

Directed Graduate Research
OPTI 792 (Spring 2016) 
Dissertation
OPTI 920 (Spring 2016) 
Independent Study
OPTI 599 (Spring 2016)
Scholarly Contributions
Books
 Anderson, B. P. (2019). SPIE Field Guide to Quantum Mechanics. SPIE.More infoA field guide to Quantum Mechanics
Journals/Publications
 Richardson, L., Hines, A., Schaffer, A., Anderson, B. P., & Guzman, F. (2020). Quantum hybrid optomechanical inertial sensing. Appl. Opt., 59(22), G160G166.
 Cawte, M. M., Yu, X., Anderson, B. P., & Bradley, A. S. (2019). Snell's Law for a vortex dipole in a BoseEinstein condensate. SCIPOST PHYSICS, 6(3).
 Kevrekidis, P. G., Wang, W., Theocharis, G., Frantzeskakis, D. J., CarreteroGonzalez, R., & Anderson, B. P. (2019). Dynamics of interacting dark soliton stripes. PHYSICAL REVIEW A, 100(3).
 , M. M., , X. Y., , B. P., & , A. S. (2018). Snell's Law for a vortex dipole in a BoseEinstein condensate.More infoA quantum vortex dipole, comprised of a closely bound pair of vortices ofequal strength with opposite circulation, is a spatially localized travellingexcitation of a planar superfluid that carries linear momentum, suggesting apossible analogy with ray optics. We investigate numerically and analyticallythe motion of a quantum vortex dipole incident upon a stepchange in thebackground superfluid density of an otherwise uniform twodimensionalBoseEinstein condensate. Due to the conservation of fluid momentum and energy,the incident and refracted angles of the dipole satisfy a relation analogous toSnell's law, when crossing the interface between regions of different density.The predictions of the analogue Snell's law relation are confirmed for a widerange of incident angles by systematic numerical simulations of theGrossPiteavskii equation. Near the critical angle for total internalreflection, we identify a regime of anomalous Snell's law behaviour where thefinite size of the dipole causes transient capture by the interface.Remarkably, despite the extra complexity of the surface interaction, theincoming and outgoing dipole paths obey Snell's law.[Journal_ref: ]
 Gertjerenken, B., Kevrekidis, P. G., CarreteroGonzalez, R., & Anderson, B. P. (2016). Generating and manipulating quantized vortices ondemand in a BoseEinstein condensate: A numerical study. PHYSICAL REVIEW A, 93(2).
 Samson, E. C., Wilson, K. E., Newman, Z. L., & Anderson, B. P. (2016). Deterministic creation, pinning, and manipulation of quantized vortices in a BoseEinstein condensate. PHYSICAL REVIEW A, 93(2).
 Vocke, D., Wilson, K., Marino, F., Carusotto, I., Wright, E. M., Roger, T., Anderson, B. P., Ohberg, P., & Faccio, D. (2016). Role of geometry in the superfluid flow of nonlocal photon fluids. PHYSICAL REVIEW A, 94(1).
 Reeves, M. T., Billam, T. P., Anderson, B. P., & Bradley, A. S. (2015). Identifying a Superfluid Reynolds Number via Dynamical Similarity. PHYSICAL REVIEW LETTERS, 114(15).
 Wilson, K. E., Newman, Z. L., Lowney, J. D., & Anderson, B. P. (2015). In situ imaging of vortices in BoseEinstein condensates. PHYSICAL REVIEW A, 91(2).
 Billam, T. P., Reeves, M. T., Anderson, B. P., & Bradley, A. S. (2014). OnsagerKraichnan Condensation in Decaying TwoDimensional Quantum Turbulence. PHYSICAL REVIEW LETTERS, 112(14).More infoDespite the prominence of Onsager's pointvortex model as a statistical description of 2D classical turbulence, a firstprinciples development of the model for a realistic superfluid has remained an open problem. Here we develop a mapping of a system of quantum vortices described by the homogeneous 2D GrossPitaevskii equation (GPE) to the pointvortex model, enabling Monte Carlo sampling of the vortex microcanonical ensemble. We use this approach to survey the full range of vortex states in a 2D superfluid, from the vortexdipole gas at positive temperature to negativetemperature states exhibiting both macroscopic vortex clustering and kinetic energy condensation, which we term an OnsagerKraichnan condensate (OKC). Damped GPE simulations reveal that such OKC states can emerge dynamically, via aggregation of smallscale clusters into giant OKC clusters, as the end states of decaying 2D quantum turbulence in a compressible, finitetemperature superfluid. These statistical equilibrium states should be accessible in atomic BoseEinstein condensate experiments.
 Reeves, M. T., Billam, T. P., Anderson, B. P., & Bradley, A. S. (2014). Signatures of coherent vortex structures in a disordered twodimensional quantum fluid. PHYSICAL REVIEW A, 89(5).More infoThe emergence of coherent rotating structures is a phenomenon characteristic of both classical and quantum twodimensional (2D) turbulence. In this work we show theoretically that the coherent vortex structures that emerge in decaying 2D quantum turbulence can approach quasiclassical rigidbody rotation, obeying the Feynman rule of constant average areal vortex density while remaining spatially disordered. By developing a rigorous link between the velocity probability distribution and the quantum kinetic energy spectrum over wave number k, we show that the coherent vortex structures are associated with a k(3) power law in the infrared region of the spectrum, and a welldefined spectral peak that is a physical manifestation of the largest structures. We discuss the possibility of realizing coherent structures in BoseEinstein condensate experiments and present GrossPitaevskii simulations showing that this phenomenon, and its associated spectral signatures, can emerge dynamically from feasible initial vortex configurations.
 White, A. C., Anderson, B. P., & Bagnato, V. S. (2014). Vortices and turbulence in trapped atomic condensates. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 111, 47194726.
 Wilson, K. E., Samson, E. C., Newman, Z. L., Neely, T. W., Anderson, B. P., Madison, K., Wang, Y., Rey, A., & Bongs, K. (2014). EXPERIMENTAL METHODS FOR GENERATING TWODIMENSIONAL QUANTUM TURBULENCE IN BOSEEINSTEIN CONDENSATES. ANNUAL REVIEW OF COLD ATOMS AND MOLECULES, VOL 1, 1, 261298.More infoBoseEinstein condensates of dilute gases are wellsuited for investigations of vortex dynamics and turbulence in quantum fluids, yet there has been little experimental research into the approaches that may be most promising for generating states of twodimensional turbulence in these systems. Here we give an overview of techniques for generating the large and disordered vortex distributions associated with twodimensional quantum turbulence. We focus on describing methods explored in our BoseEinstein condensation laboratory, and discuss the suitability of these methods for studying various aspects of twodimensional quantum turbulence. We also summarize some of the open questions regarding our own understanding of these mechanisms of twodimensional quantum turbulence generation in condensates. We find that while these disordered distributions of vortices can be generated by a variety of techniques, further investigation is needed to identify methods for obtaining quasisteadystate quantum turbulence in condensates.
 Kuopanportti, P., Anderson, B. P., & Möttönen, M. (2013). Vortex pump for BoseEinstein condensates utilizing a timeaveraged orbiting potential trap. Physical Review A  Atomic, Molecular, and Optical Physics, 87(3).More infoAbstract: We show that topological vortex pumping can be implemented for a dilute BoseEinstein condensate confined in a magnetic timeaveraged orbiting potential trap with axial optical confinement. Contrary to earlier proposals for the vortex pump, we do not employ an additional optical potential to trap the condensate in the radial direction, but instead, the radial confinement is provided by the magnetic field throughout the pumping cycle. By performing numerical simulations based on the spin1 GrossPitaevskii equation, we find that several pumping cycles can be carried out to produce a highly charged vortex before a majority of the particles escape from the trap or before the vortex splits into singly charged vortices. On the other hand, we observe that an additional, relatively weak optical plug potential is efficient in preventing splitting and reducing particle loss. With these results, we hope to bring the vortex pump closer to experimental realization. © 2013 American Physical Society.
 Law, K. J., Neely, T. W., Kevrekidis, P. G., Anderson, B. P., Bradley, A. S., & CarreteroGonzalez, R. (2014). Dynamic and energetic stabilization of persistent currents in BoseEinstein condensates. PHYSICAL REVIEW A, 89(5).More infoWe study conditions under which vortices in a highly oblate harmonically trapped BoseEinstein condensate (BEC) can be stabilized due to pinning by a bluedetuned Gaussian laser beam, with particular emphasis on the potentially destabilizing effects of laser beam positioning within the BEC. Our approach involves theoretical and numerical exploration of dynamically and energetically stable pinning of vortices with winding number up to S = 6, in correspondence with experimental observations. Stable pinning is quantified theoretically via Bogoliubovde Gennes excitation spectrum computations and confirmed via direct numerical simulations for a range of conditions similar to those of experimental observations. The theoretical and numerical results indicate that the pinned winding number, or equivalently the winding number of the superfluid current about the laser beam, decays as a laser beam of fixed intensity moves away from the BEC center. Our theoretical analysis helps explain previous experimental observations and helps define limits of stable vortex pinning for future experiments involving vortex manipulation by laser beams.
 Neely, T. W., Bradley, A. S., Samson, E. C., Rooney, S. J., Wright, E. M., Law, K. J., CarreteroGonzález, R., Kevrekidis, P. G., Davis, M. J., & Anderson, B. P. (2013). Characteristics of twodimensional quantum turbulence in a compressible superfluid. Physical Review Letters, 111(23).More infoAbstract: Fluids subjected to suitable forcing will exhibit turbulence, with characteristics strongly affected by the fluid's physical properties and dimensionality. In this work, we explore twodimensional (2D) quantum turbulence in an oblate BoseEinstein condensate confined to an annular trapping potential. Experimentally, we find conditions for which smallscale stirring of the condensate generates disordered 2D vortex distributions that dissipatively evolve toward persistent currents, indicating energy transport from small to large length scales. Simulations of the experiment reveal spontaneous clustering of samecirculation vortices and an incompressible energy spectrum with k 5/3 dependence for low wave numbers k. This work links experimentally observed vortex dynamics with signatures of 2D turbulence in a compressible superfluid. © 2013 American Physical Society.
 Reeves, M. T., Billam, T. P., Anderson, B. P., & Bradley, A. S. (2013). Inverse energy cascade in forced twodimensional quantum turbulence. Physical Review Letters, 110(10).More infoAbstract: We demonstrate an inverse energy cascade in a minimal model of forced 2D quantum vortex turbulence. We simulate the GrossPitaevskii equation for a moving superfluid subject to forcing by a stationary grid of obstacle potentials, and damping by a stationary thermal cloud. The forcing injects large amounts of vortex energy into the system at the scale of a few healing lengths. A regime of forcing and damping is identified where vortex energy is efficiently transported to large length scales via an inverse energy cascade associated with the growth of clusters of samecirculation vortices, a Kolmogorov scaling law in the kinetic energy spectrum over a substantial inertial range, and spectral condensation of kinetic energy at the scale of the system size. Our results provide clear evidence that the inverse energy cascade phenomenon, previously observed in a diverse range of classical systems, can also occur in quantum fluids. © 2013 American Physical Society.
 Rooney, S. J., Neely, T. W., Anderson, B. P., & Bradley, A. S. (2013). Persistentcurrent formation in a hightemperature BoseEinstein condensate: An experimental test for classicalfield theory. Physical Review A  Atomic, Molecular, and Optical Physics, 88(6).More infoAbstract: Experimental stirring of a toroidally trapped BoseEinstein condensate at high temperature generates a disordered array of quantum vortices that decays via thermal dissipation to form a macroscopic persistent current. We perform threedimensional numerical simulations of the experimental sequence within the stochastic projected GrossPitaevskii equation using ab initio determined reservoir parameters. We find that both damping and noise are essential for describing the dynamics of the hightemperature Bose field. The theory gives a quantitative account of the formation of a persistent current, with no fitted parameters. © 2013 American Physical Society.
 Bradley, A. S., & Anderson, B. P. (2012). Energy spectra of vortex distributions in twoDimensional quantum turbulence. Physical Review X, 2(4).More infoAbstract: We theoretically explore key concepts of twodimensional turbulence in a homogeneous compressible superfluid described by a dissipative twodimensional GrossPitaeveskii equation. Such a fluid supports quantized vortices that have a size characterized by the healing length ξ.We show that, for the divergencefree portion of the superfluid velocity field, the kineticenergy spectrum over wave number k may be decomposed into an ultraviolet regime (k ≫ ξ1) having a universal k3 scaling arising from the vortex core structure, and an infrared regime (k ≪ ξ1) with a spectrum that arises purely from the configuration of the vortices. The Novikov powerlaw distribution of intervortex distances with exponent 1/3 for vortices of the same sign of circulation leads to an infrared kineticenergy spectrum with a Kolmogorov k5/3 power law, which is consistent with the existence of an inertial range. The presence of these k3 and k5/3 power laws, together with the constraint of continuity at the smallest configurational scale k ≈ ξ1, allows us to derive a new analytical expression for the Kolmogorov constant that we test against a numerical simulation of a forced homogeneous, compressible, twodimensional superfluid. The numerical simulation corroborates our analysis of the spectral features of the kineticenergy distribution, once we introduce the concept of a clustered fraction consisting of the fraction of vortices that have the same sign of circulation as their nearest neighboring vortices. Our analysis presents a new approach to understanding twodimensional quantum turbulence and interpreting similarities and differences with classical twodimensional turbulence, and suggests new methods to characterize vortex turbulence in twodimensional quantum fluids via vortex position and circulation measurements.
 Reeves, M. T., Anderson, B. P., & Bradley, A. S. (2012). Classical and quantum regimes of twodimensional turbulence in trapped BoseEinstein condensates. Physical Review A  Atomic, Molecular, and Optical Physics, 86(5).More infoAbstract: We investigate twodimensional turbulence in finitetemperature trapped BoseEinstein condensates within damped GrossPitaevskii theory. Turbulence is produced via circular motion of a Gaussian potential barrier stirring the condensate. We systematically explore a range of stirring parameters and identify three regimes, characterized by the injection of distinct quantum vortex structures into the condensate: (A) periodic vortex dipole injection, (B) irregular injection of a mixture of vortex dipoles and corotating vortex clusters, and (C) continuous injection of oblique solitons that decay into vortex dipoles. Spectral analysis of the kinetic energy associated with vortices reveals that regime (B) can intermittently exhibit a Kolmogorov k 5/3 power law over almost a decade of length or wavenumber (k) scales. The kinetic energy spectrum of regime (C) exhibits a clear k3/2 power law associated with an inertial range for weakwave turbulence and a k7/2 power law for high wave numbers. We thus identify distinct regimes of forcing for generating either twodimensional quantum turbulence or classical weakwave turbulence that may be realizable experimentally. © 2012 American Physical Society.
 Anderson, B. P., Neely, T. W., Bradley, A. S., Samson, E. C., Rooney, S. J., Wright, E. M., Law, K. J., CarreteroGonzález, R., Kevrekidis, P. G., & Davis, M. J. (2011). Twodimensional quantum turbulence in BoseEinstein condensates. 2011 Int. Quantum Electron. Conf., IQEC 2011 and Conf. Lasers and ElectroOptics, CLEO Pacific Rim 2011 Incorporating the Australasian Conf. Optics, Lasers and Spectroscopy and the Australian Conf., 1071.More infoAbstract: We report the experimental generation of twodimensional quantum turbulence in dilutegas BoseEinstein condensates by stirring the condensate with a laser beam, and the decay of the turbulent state to a largescale flow in the form of a persistent current in a toroidal trap geometry. From numerical simulations of the stirring process, we characterize the dynamics of the quantized vortices in the condensate, and analyze the kinetic energy spectrum. Our observations are consistent with basic features of twodimensional turbulence in classical incompressible fluids. © 2011 IEEE.
 Anderson, B. P., Neely, T. W., Bradley, A. S., Samson, E. C., Rooney, S. J., Wright, E. M., Law, K. J., CarreteroGonzález, R., Kevrekidis, P. G., & Davis, M. J. (2011). Twodimensional quantum turbulence in boseeinstein condensates. Optics InfoBase Conference Papers, 1071.More infoAbstract: We report the experimental generation of twodimensional quantum turbulence in dilutegas BoseEinstein condensates by stirring the condensate with a laser beam, and the decay of the turbulent state to a largescale flow in the form of a persistent current in a toroidal trap geometry. From numerical simulations of the stirring process, we characterize the dynamics of the quantized vortices in the condensate, and analyze the kinetic energy spectrum. Our observations are consistent with basic features of twodimensional turbulence in classical incompressible fluids. © 2011 AOS.
 Rooney, S. J., Blakie, P. B., Anderson, B. P., & Bradley, A. S. (2011). Suppression of Kelvoninduced decay of quantized vortices in oblate BoseEinstein condensates. Physical Review A  Atomic, Molecular, and Optical Physics, 84(2).More infoAbstract: We study the Kelvin mode excitations on a vortex line in a threedimensional trapped BoseEinstein condensate at finite temperature. Our stochastic GrossPitaevskii simulations show that the activation of these modes can be suppressed by tightening the confinement along the direction of the vortex line, leading to a strong suppression in the vortex decay rate as the system enters a regime of twodimensional vortex dynamics. As the system approaches the condensation transition temperature, we find that the vortex decay rate is strongly sensitive to dimensionality and temperature, observing a large enhancement for quasitwodimensional traps. Threedimensional simulations of the recent vortex dipole decay experiment of Neely confirm twodimensional vortex dynamics and predict a dipole lifetime consistent with experimental observations and suppression of Kelvoninduced vortex decay in highly oblate condensates. © 2011 American Physical Society.
 Anderson, B. P. (2010). Resource article: Experiments with vortices in superfluid atomic gases. Journal of Low Temperature Physics, 161(56), 574602.More infoAbstract: Observations of quantized vortices in dilutegas BoseEinstein condensates were first reported in 1999. Over the next 10 years, more than 70 papers describing experiments involving vortices in superfluid atomic gases were published in scientific journals. This resource article provides a guide to the published experimental studies related to quantized vortices in atomic BoseEinstein condensates and superfluid Fermi gases. A BibTexformatted bibliography document listing these published studies is also available electronically. © Springer Science+Business Media, LLC 2010.
 Neely, T. W., Samson, E. C., Bradley, A. S., Davis, M. J., & Anderson, B. P. (2010). Observation of vortex dipoles in an oblate BoseEinstein condensate. Physical Review Letters, 104(16).More infoAbstract: We report experimental observations and numerical simulations of the formation, dynamics, and lifetimes of single and multiply charged quantized vortex dipoles in highly oblate dilutegas BoseEinstein condensates (BECs). We nucleate pairs of vortices of opposite charge (vortex dipoles) by forcing superfluid flow around a repulsive Gaussian obstacle within the BEC. By controlling the flow velocity we determine the critical velocity for the nucleation of a single vortex dipole, with excellent agreement between experimental and numerical results. We present measurements of vortex dipole dynamics, finding that the vortex cores of opposite charge can exist for many seconds and that annihilation is inhibited in our trap geometry. For sufficiently rapid flow velocities, clusters of likecharge vortices aggregate into longlived multiply charged dipolar flow structures. © 2010 The American Physical Society.
 Davis, M. C., CarreteroGonzález, R., Shi, Z., Law, K. J., Kevrekidis, P. G., & Anderson, B. P. (2009). Manipulation of vortices by localized impurities in BoseEinstein condensates. Physical Review A  Atomic, Molecular, and Optical Physics, 80(2).More infoAbstract: We consider the manipulation of BoseEinstein condensate vortices by optical potentials generated by focused laser beams. It is shown that for appropriate choices of the laser strength and width it is possible to successfully transport vortices to various positions inside the trap confining the condensate atoms. Furthermore, the full bifurcation structure of possible stationary singlecharge vortex solutions in a harmonic potential with this type of impurity is elucidated. The case when a moving vortex is captured by a stationary laser beam is also studied, as well as the possibility of dragging the vortex by means of periodic optical lattices. © 2009 The American Physical Society.
 CarreteroGonzález, R., Anderson, B. P., Kevrekidis, P. G., Frantzeskakis, D. J., & Weiler, C. N. (2008). Dynamics of vortex formation in merging BoseEinstein condensate fragments. Physical Review A  Atomic, Molecular, and Optical Physics, 77(3).More infoAbstract: We study the formation of vortices in a BoseEinstein condensate (BEC) that has been prepared by allowing isolated and independent condensed fragments to merge together. We focus on the experimental setup of Scherer [Phys. Rev. Lett. 98, 110402 (2007)], where three BECs are created in a magnetic trap that is segmented into three regions by a repulsive optical potential; the BECs merge together as the optical potential is removed. First, we study the twodimensional case; in particular, we examine the effects of the relative phases of the different fragments and the removal rate of the optical potential on the vortex formation. We find that many vortices are created by instant removal of the optical potential regardless of relative phases, and that fewer vortices are created if the intensity of the optical potential is gradually ramped down and the condensed fragments gradually merge. In all cases, selfannihilation of vortices of opposite charge is observed. We also find that for sufficiently long barrier ramp times, the initial relative phases between the fragments leave a clear imprint on the resulting topological configuration. Finally, we study the threedimensional system and the formation of vortex lines and vortex rings due to the merger of the BEC fragments; our results illustrate how the relevant vorticity is manifested for appropriate phase differences, as well as how it may be masked by the planar projections observed experimentally. © 2008 The American Physical Society.
 Law, K. J., Kevrekidis, P. G., Anderson, B. P., CarreteroGonzález, R., & Frantzeskakis, D. J. (2008). Structure and stability of twodimensional BoseEinstein condensates under both harmonic and lattice confinement. Journal of Physics B: Atomic, Molecular and Optical Physics, 41(19).More infoAbstract: In this work, we study twodimensional BoseEinstein condensates confined by both a cylindrically symmetric harmonic potential and an optical lattice with equal periodicity in two orthogonal directions. We first identify the spectrum of the underlying twodimensional linear problem through multiplescale techniques. Then, we use the results obtained in the linear limit as a starting point for the existence and stability analysis of the lowest energy states, emanating from the linear ones, in the nonlinear problem. Twoparameter continuations of these states are performed for increasing nonlinearity and optical lattice strengths, and their instabilities and temporal evolution are investigated. It is found that the ground state as well as some of the excited states may be stable or weakly unstable for both attractive and repulsive interatomic interactions. Higher excited states are typically found to be increasingly more unstable. © 2008 IOP Publishing Ltd.
 Weiler, C. N., Neely, T. W., Scherer, D. R., Bradley, A. S., Davis, M. J., & Anderson, B. P. (2008). Spontaneous vortices in the formation of BoseEinstein condensates. Nature, 455(7215), 948951.More infoAbstract: Phase transitions are ubiquitous in nature, and can be arranged into universality classes such that systems having unrelated microscopic physics show identical scaling behaviour near the critical point. One prominent universal element of many continuous phase transitions is the spontaneous formation of topological defects during a quench through the critical point. The microscopic dynamics of defect formation in such transitions are generally difficult to investigate, particularly for superfluids. However, BoseEinstein condensates (BECs) offer unique experimental and theoretical opportunities for probing these details. Here we present an experimental and theoretical study of the BEC phase transition of a trapped atomic gas, in which we observe and statistically characterize the spontaneous formation of vortices during condensation. Using microscopic theories that incorporate atomic interactions and quantum and thermal fluctuations of a finitetemperature Bose gas, we simulate condensation and observe vortex formation in close quantitative agreement with our experimental results. Our studies provide further understanding of the development of coherence in superfluids, and may allow for direct investigation of universal phase transition dynamics. ©2008 Macmillan Publishers Limited. All rights reserved.
 Scherer, D. R., Weiler, C. N., Neely, T. W., & Anderson, B. P. (2007). Vortex formation by merging of multiple trapped boseeinstein condensates. Physical Review Letters, 98(11).More infoAbstract: We report observations of vortex formation by merging and interfering multiple Rb87 BoseEinstein condensates (BECs) in a confining potential. In this experiment, a single harmonic potential well is partitioned into three sections by a barrier, enabling the simultaneous formation of three independent, uncorrelated BECs. The BECs may either automatically merge together during their growth, or for highenergy barriers, the BECs can be merged together by barrier removal after their formation. Either process may instigate vortex formation in the resulting BEC, depending on the initially indeterminate relative phases of the condensates and the merging rate. © 2007 The American Physical Society.
 Anderson, B. P., Dholakia, K., & Wright, E. M. (2003). Atomicphase interference devices based on ringshaped BoseEinstein condensates: Tworing case. Physical Review A  Atomic, Molecular, and Optical Physics, 67(3), 033601/1033601/8.More infoAbstract: A theoretical investigation of a pair of ring BoseEinstein condensates (BECs) coupled by tunneling as the simplest example of a potential atomicphase interference device (APHID) is presented. It is shown that the tworing APHID has interesting groundstate properties, with density profiles reminiscent of dark soliton states around the point of contact of the rings. Furthermore, it is demonstrated that Josephson oscillations between the two rings can occur, and that these oscillations are sensitive to the state of rotation of the APHID.
 Anderson, B. P., & Kasevich, M. A. (2001). Loading a vaporcell magnetooptic trap using lightinduced atom desorption. Physical Review A  Atomic, Molecular, and Optical Physics, 63(2), 16.More infoAbstract: Lowintensity white light was used to increase the loading rate of 87Rb atoms into a vaporcell magnetooptic trap by inducing nonthermal desorption of Rb atoms from the stainlesssteel walls of the vapor cell. An increased Rb partial pressure reached a new equilibrium value in fewer than 10 s after switching on the broadband light source. After the source was turned off, the partial pressure returned to its previous value in 1/e times as short as 10 s. ©2001 The American Physical Society.
 Anderson, B. P., Haljan, P. C., Regal, C. A., Feder, D. L., Collins, L. A., Clark, C. W., & Cornell, E. A. (2001). Watching dark solitons decay into vortex rings in a BoseEinstein condensate. Physical Review Letters, 86(14), 29262929.More infoPMID: 11290074;Abstract: Dark solitons were created in twocomponent BoseEinstein condensates, where the soliton exists in one of the condensate components and the soliton nodal plane is filled with the second component. The filled solitons are stable for hundreds of milliseconds. The filling can be selectively removed, making the soliton more susceptible to dynamical instabilities. For a condensate in a spherically symmetric potential, these instabilities cause the dark soliton to decay into stable vortex rings.
 Haljan, P. C., Anderson, B. P., Coddington, I., & Comell, E. A. (2001). Use of surfacewave spectroscopy to characterize tilt modes of a vortex in a BoseEinstein condensate. Physical Review Letters, 86(14), 29222925.More infoPMID: 11290073;Abstract: A nondestructive method of vortex detection was described and was used to characterize the tilt modes of a bare vortex in a trapped BoseEinstein condensate (BEC). Control over the tilt of a vortex was demonstrated, including the suppression of tilting altogether. The suppression of tilting, which maintains the visibility of vortices out to long times, permits the study of the lifetime of vortices at finite temperature.
 Anderson, B. P., Haljan, P. C., Wieman, C. E., & Cornell, E. A. (2000). Vortex precession in BoseEinstein condensates: observations with filled and empty cores. Physical Review Letters, 85(14), 28572860.More infoPMID: 11005953;Abstract: Vortex dynamics in bare and filledcore vortices in dilutegas BoseEinstein condensates (BECs) were measured using a combination of destructive and nondestructive imaging techniques. Vortex precision frequencies showed only modest dependence on the radius and content of the vortex core.
 Haljan, P. C., Anderson, B. P., Matthews, M. R., Hall, D. S., Wieman, C. E., & Cornell, E. A. (2000). Vortices in a Bose Einstein Condensate. Conference on Quantum Electronics and Laser Science (QELS)  Technical Digest Series, 201202.More infoAbstract: Using a method proposed by Williams and Holland, an attempt was made to prepare vortices, macroscopic quantum states with quantized angular momentum in trapped BEC of 87Rb. A coupling field allows interconversion between twocomponent condensates.
 Haljan, P. C., Anderson, B. P., Wieman, C. E., & Cornell, E. A. (2000). Using surface excitations to detect bare vortices in a BoseEinstein condensate. Conference on Quantum Electronics and Laser Science (QELS)  Technical Digest Series, 291292.More infoAbstract: The lifetime and dynamics of vortices in a BoseEinstein condensate (BEC) of dilute atomic vapor can shed light on the superfluid character of BEC in alkalis. An overview is given on the various efforts at preparing such vortices. Focus is on an alternative method of vortex detection which should be less sensitive to deformation of the vortex line.
 Anderson, B. P., & Kasevich, M. A. (1999). Spatial observation of BoseEinstein condensation of ^{87}Rb in a confining potential. Physical Review A  Atomic, Molecular, and Optical Physics, 59(23), R938R941.More infoAbstract: BoseEinstein condensation of 87Rb has been observed in a vapor cell timeaveraged orbiting potential trap, and the trapped condensates have been studied using in situ absorption and darkground imaging methods. Condensates of 3 × 104 atoms were observed after 26 s of evaporative cooling. The evaporative cooling sequence consisted of a combination of cooling with ramping magneticfield strengths and radiofrequencyinduced cooling. The measured sizes, numbers of atoms, and transition temperatures of the condensates are consistent with theoretical predictions that include the effects of atomic interactions.
 Anderson, B., Gustavson, T., Landragin, A., McGuirk, J., Snadden, M., Yasuda, M., & Kasevich, M. (1999). Precision atom interferometry. Journal of the Communications Research Laboratory, 46(3), 449451.More infoAbstract: Recent progress in the development of atom interferometerbased gyroscopes, accelerometers and gravity gradiometers will be presented.
 Matthews, M. R., Anderson, B. P., Haljan, P. C., Hall, D. S., Holland, M. J., Williams, J. E., Wieman, C. E., & Cornell, E. A. (1999). Watching a Superfluid Untwist Itself: Recurrence of Rabi Oscillations in a BoseEinstein Condensate. Physical Review Letters, 83(17), 33583361.More infoAbstract: The order parameter of a condensate with two internal states can continuously distort in such a way as to remove twists that have been imposed along its length. We observe this effect experimentally in the collapse and recurrence of Rabi oscillations in a magnetically trapped, twocomponent BoseEinstein condensate of 87Rb.
 Matthews, M. R., Anderson, B. P., Haljan, P. C., Hall, D. S., Wieman, C. E., & Cornell, E. A. (1999). Vortices in a boseeinstein condensate. Physical Review Letters, 83(13), 24982501.More infoAbstract: We have created vortices in twocomponent BoseEinstein condensâtes. The vortex state was created through a coherent process involving the spatial and temporal control of interconversion between the two components. Using an interference technique, we map the phase of the vortex state to confirm that it possesses angular momentum. We can create vortices in either of the two components and have observed differences in the dynamics and stability. © 1999 The American Physical Society.
 Anderson, B. P., & Kasevich, M. A. (1998). Macroscopic quantum interference from atomic tunnel arrays. Science, 282(5394), 16861689.More infoAbstract: 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.
 Anderson, B. P., Gustavson, T. L., & Kasevich, M. A. (1996). Atom trapping in nondissipative optical lattices. Physical Review A  Atomic, Molecular, and Optical Physics, 53(6), R3727R3730.More infoAbstract: Lasercooled 7Li atoms have been confined in threedimensional spatially periodic potentials that are nearly conservative. The potentials were formed from the intersection of four laser beams fardetuned from the optical resonance. By adjusting the relative orientations of the beams, lattices with primitive translation vectors larger than the laser light wavelength were created. We achieved an effective temperature of ∼80 μK through adiabatic reduction of the confining potential strength, and prepared ensembles with effective temperatures of ∼1.8 μK by initially confining atoms in weak potentials.
 Anderson, B. P., & Kasevich, M. A. (1994). Enhanced loading of a magnetooptic trap from an atomic beam. Physical Review A, 50(5), R3581R3584.More infoAbstract: We demonstrate enhanced loading of a Li7 magnetooptic trap by broadening the frequency spectrum of the laser trapping light with a resonant electrooptic modulator. We achieve an 20fold improvement in the loading rate over that obtained without a broadened spectrum when directly capturing atoms from a divergent atomic beam. © 1994 The American Physical Society.