# Publications by Robert Smith

## Universal Prethermal Dynamics of Bose Gases Quenched to Unitarity

Nature Nature Publishing Group 563 (2018) 221-224

C Eigen, JAP Glidden, R Lopes, EA Cornell, RP Smith, Z Hadzibabic

Understanding strongly correlated phases of matter, from the quark-gluon plasma to neutron stars, and in particular the dynamics of such systems, e.g. following a Hamiltonian quench, poses a fundamental challenge in modern physics. Ultracold atomic gases are excellent quantum simulators for these problems, thanks to tuneable interparticle interactions and experimentally resolvable intrinsic timescales. In particular, they give access to the unitary regime where the interactions are as strong as allowed by quantum mechanics. Following years of experiments on unitary Fermi gases, unitary Bose gases have recently emerged as a new experimental frontier. They promise exciting new possibilities, including universal physics solely controlled by the gas density and novel forms of superfluidity. Here, through momentum- and time-resolved studies, we explore both degenerate and thermal homogeneous Bose gases quenched to unitarity. In degenerate samples we observe universal post-quench dynamics in agreement with the emergence of a prethermal state with a universal nonzero condensed fraction. In thermal gases, dynamic and thermodynamic properties generically depend on both the gas density n and temperature T, but we find that they can still be expressed in terms of universal dimensionless functions. Surprisingly, the total quench-induced correlation energy is independent of the gas temperature. Our measurements provide quantitative benchmarks and new challenges for theoretical understanding.

## Elliptic flow in a strongly interacting normal Bose gas

PHYSICAL REVIEW A 98 (2018) ARTN 011601

RJ Fletcher, J Man, R Lopes, P Christodoulou, J Schmitt, M Sohmen, N Navon, RP Smith, Z Hadzibabic

## Quantum Depletion of a Homogeneous Bose-Einstein Condensate.

Phys Rev Lett 119 (2017) 190404-

R Lopes, C Eigen, N Navon, D Clément, RP Smith, Z Hadzibabic

We measure the quantum depletion of an interacting homogeneous Bose-Einstein condensate and confirm the 70-year-old theory of Bogoliubov. The observed condensate depletion is reversibly tunable by changing the strength of the interparticle interactions. Our atomic homogeneous condensate is produced in an optical-box trap, the interactions are tuned via a magnetic Feshbach resonance, and the condensed fraction is determined by momentum-selective two-photon Bragg scattering.

## Two- and three-body contacts in the unitary Bose gas.

Science (New York, N.Y.) 355 (2017) 377-380

RJ Fletcher, R Lopes, J Man, N Navon, RP Smith, MW Zwierlein, Z Hadzibabic

In many-body systems governed by pairwise contact interactions, a wide range of observables is linked by a single parameter, the two-body contact, which quantifies two-particle correlations. This profound insight has transformed our understanding of strongly interacting Fermi gases. Using Ramsey interferometry, we studied coherent evolution of the resonantly interacting Bose gas, and we show here that it cannot be explained by only pairwise correlations. Our experiments reveal the crucial role of three-body correlations arising from Efimov physics and provide a direct measurement of the associated three-body contact.

## Universal Scaling Laws in the Dynamics of a Homogeneous Unitary Bose Gas.

Phys Rev Lett 119 (2017) 250404-

C Eigen, JAP Glidden, R Lopes, N Navon, Z Hadzibabic, RP Smith

We study the dynamics of an initially degenerate homogeneous Bose gas after an interaction quench to the unitary regime at a magnetic Feshbach resonance. As the cloud decays and heats, it exhibits a crossover from degenerate- to thermal-gas behavior, both of which are characterized by universal scaling laws linking the particle-loss rate to the total atom number N. In the degenerate and thermal regimes, the per-particle loss rate is ∝N^{2/3} and N^{26/9}, respectively. The crossover occurs at a universal kinetic energy per particle and at a universal time after the quench, in units of energy and time set by the gas density. By slowly sweeping the magnetic field away from the resonance and creating a mixture of atoms and molecules, we also map out the dynamics of correlations in the unitary gas, which display a universal temporal scaling with the gas density, and reach a steady state while the gas is still degenerate.

## Effects of interactions on Bose-Einstein condensation

in Universal Themes of Bose-Einstein Condensation, (2017) 99-116

RP Smith

© Nick P. Proukakis, David W. Snoke and Peter B. Littlewood 2017. All rights reserved. Bose-Einstein condensation is a unique phase transition in that it is not driven by interparticle interactions, but can theoretically occur in an ideal gas, purely as a consequence of quantum statistics. This chapter addresses the question, 'How is this ideal Bose gas condensation modified in the presence of interactions between the particles?' This seemingly simple question turns out to be surprisingly difficult to answer. Here we outline the theoretical background to this question and discuss some recent measurements on ultracold atomic Bose gases that have sought to provide some answers.

## Quasiparticle Energy in a Strongly Interacting Homogeneous Bose-Einstein Condensate.

Phys Rev Lett 118 (2017) 210401-

R Lopes, C Eigen, A Barker, KGH Viebahn, M Robert-de-Saint-Vincent, N Navon, Z Hadzibabic, RP Smith

Using two-photon Bragg spectroscopy, we study the energy of particlelike excitations in a strongly interacting homogeneous Bose-Einstein condensate, and observe dramatic deviations from Bogoliubov theory. In particular, at large scattering length a the shift of the excitation resonance from the free-particle energy changes sign from positive to negative. For an excitation with wave number q, this sign change occurs at a≈4/(πq), in agreement with the Feynman energy relation and the static structure factor expressed in terms of the two-body contact. For a≳3/q we also see a breakdown of this theory, and better agreement with calculations based on the Wilson operator product expansion. Neither theory explains our observations across all interaction regimes, inviting further theoretical efforts.

## Observation of weak collapse in a Bose-Einstein condensate

Physical Review X 6 (2016)

C Eigen, AL Gaunt, A Suleymanzade, N Navon, Z Hadzibabic, RP Smith

We study the collapse of an attractive atomic Bose-Einstein condensate prepared in the uniform potential of an optical-box trap. We characterize the critical point for collapse and the collapse dynamics, observing universal behavior in agreement with theoretical expectations. Most importantly, we observe a clear experimental signature of the counterintuitive weak collapse, namely, that making the system more unstable can result in a smaller particle loss. We experimentally determine the scaling laws that govern the weak-collapse atom loss, providing a benchmark for the general theories of nonlinear wave phenomena.

## Emergence of a turbulent cascade in a quantum gas.

Nature 539 (2016) 72-75

N Navon, AL Gaunt, RP Smith, Z Hadzibabic

A central concept in the modern understanding of turbulence is the existence of cascades of excitations from large to small length scales, or vice versa. This concept was introduced in 1941 by Kolmogorov and Obukhov, and such cascades have since been observed in various systems, including interplanetary plasmas, supernovae, ocean waves and financial markets. Despite much progress, a quantitative understanding of turbulence remains a challenge, owing to the interplay between many length scales that makes theoretical simulations of realistic experimental conditions difficult. Here we observe the emergence of a turbulent cascade in a weakly interacting homogeneous Bose gas-a quantum fluid that can be theoretically described on all relevant length scales. We prepare a Bose-Einstein condensate in an optical box, drive it out of equilibrium with an oscillating force that pumps energy into the system at the largest length scale, study its nonlinear response to the periodic drive, and observe a gradual development of a cascade characterized by an isotropic power-law distribution in momentum space. We numerically model our experiments using the Gross-Pitaevskii equation and find excellent agreement with the measurements. Our experiments establish the uniform Bose gas as a promising new medium for investigating many aspects of turbulence, including the interplay between vortex and wave turbulence, and the relative importance of quantum and classical effects.

## Superconductivity in graphite intercalation compounds

PHYSICA C-SUPERCONDUCTIVITY AND ITS APPLICATIONS 514 (2015) 50-58

RP Smith, TE Weller, CA Howard, MPM Dean, KC Rahnejat, SS Saxena, M Ellerby

## Quantum gases. Critical dynamics of spontaneous symmetry breaking in a homogeneous Bose gas.

Science (New York, N.Y.) 347 (2015) 167-170

N Navon, AL Gaunt, RP Smith, Z Hadzibabic

Kibble-Zurek theory models the dynamics of spontaneous symmetry breaking, which plays an important role in a wide variety of physical contexts, ranging from cosmology to superconductors. We explored these dynamics in a homogeneous system by thermally quenching an atomic gas with short-range interactions through the Bose-Einstein phase transition. Using homodyne matter-wave interferometry to measure first-order correlation functions, we verified the central quantitative prediction of the Kibble-Zurek theory, namely the homogeneous-system power-law scaling of the coherence length with the quench rate. Moreover, we directly confirmed its underlying hypothesis, the freezing of the correlation length near the transition. Our measurements agree with a beyond-mean-field theory and support the expectation that the dynamical critical exponent for this universality class is z = 3/2.

## Connecting Berezinskii-Kosterlitz-Thouless and BEC Phase Transitions by Tuning Interactions in a Trapped Gas.

Physical review letters 114 (2015) 255302-

RJ Fletcher, M Robert-de-Saint-Vincent, J Man, N Navon, RP Smith, KGH Viebahn, Z Hadzibabic

We study the critical point for the emergence of coherence in a harmonically trapped two-dimensional Bose gas with tunable interactions. Over a wide range of interaction strengths we find excellent agreement with the classical-field predictions for the critical point of the Berezinskii-Kosterlitz-Thouless (BKT) superfluid transition. This allows us to quantitatively show, without any free parameters, that the interaction-driven BKT transition smoothly converges onto the purely quantum-statistical Bose-Einstein condensation transition in the limit of vanishing interactions.

## Quantum Joule-Thomson effect in a saturated homogeneous Bose gas.

Physical review letters 112 (2014) 040403-

TF Schmidutz, I Gotlibovych, AL Gaunt, RP Smith, N Navon, Z Hadzibabic

We study the thermodynamics of Bose-Einstein condensation in a weakly interacting quasihomogeneous atomic gas, prepared in an optical-box trap. We characterize the critical point for condensation and observe saturation of the thermal component in a partially condensed cloud, in agreement with Einstein's textbook picture of a purely statistical phase transition. Finally, we observe the quantum Joule-Thomson effect, namely isoenthalpic cooling of an (essentially) ideal gas. In our experiments this cooling occurs spontaneously, due to energy-independent collisions with the background gas in the vacuum chamber. We extract a Joule-Thomson coefficient μJT>10(9)  K/bar, about 10 orders of magnitude larger than observed in classical gases.

## Observing properties of an interacting homogeneous Bose-Einstein condensate: Heisenberg-limited momentum spread, interaction energy, and free-expansion dynamics

PHYSICAL REVIEW A 89 (2014) ARTN 061604

I Gotlibovych, TF Schmidutz, AL Gaunt, N Navon, RP Smith, Z Hadzibabic

## Ferroelectric quantum criticality

NATURE PHYSICS 10 (2014) 367-372

SE Rowley, LJ Spalek, RP Smith, MPM Dean, M Itoh, JF Scott, GG Lonzarich, SS Saxena

## Bose-Einstein condensation of atoms in a uniform potential.

Physical review letters 110 (2013) 200406-

AL Gaunt, TF Schmidutz, I Gotlibovych, RP Smith, Z Hadzibabic

We have observed the Bose-Einstein condensation of an atomic gas in the (quasi)uniform three-dimensional potential of an optical box trap. Condensation is seen in the bimodal momentum distribution and the anisotropic time-of-flight expansion of the condensate. The critical temperature agrees with the theoretical prediction for a uniform Bose gas. The momentum distribution of a noncondensed quantum-degenerate gas is also clearly distinct from the conventional case of a harmonically trapped sample and close to the expected distribution in a uniform system. We confirm the coherence of our condensate in a matter-wave interference experiment. Our experiments open many new possibilities for fundamental studies of many-body physics.

## Stability of a unitary Bose gas.

Physical review letters 111 (2013) 125303-

RJ Fletcher, AL Gaunt, N Navon, RP Smith, Z Hadzibabic

We study the stability of a thermal (39)K Bose gas across a broad Feshbach resonance, focusing on the unitary regime, where the scattering length a exceeds the thermal wavelength λ. We measure the general scaling laws relating the particle-loss and heating rates to the temperature, scattering length, and atom number. Both at unitarity and for positive a<<λ we find agreement with three-body theory. However, for a<0 and away from unitarity, we observe significant four-body decay. At unitarity, the three-body loss coefficient, L(3) proportional λ(4), is 3 times lower than the universal theoretical upper bound. This reduction is a consequence of species-specific Efimov physics and makes (39)K particularly promising for studies of many-body physics in a unitary Bose gas.

## A superheated Bose-condensed gas

NATURE PHYSICS 9 (2013) 271-274

AL Gaunt, RJ Fletcher, RP Smith, Z Hadzibabic

## Effects of Interactions on Bose-Einstein Condensation of an Atomic Gas

in Physics of Quantum Fluids, Springer (2013) 16

## A compact single-chamber apparatus for Bose-Einstein condensation of $^87$Rb
We describe a simple and compact single-chamber apparatus for robust production of $^87$Rb Bose-Einstein condensates. The apparatus is built from off-the-shelf components and allows production of quasi-pure condensates of > $3\times 10^5$ atoms in < 30 s. This is achieved using a hybrid trap created by a quadrupole magnetic field and a single red-detuned laser beam [Y.-J. Lin et al., Phys. Rev. A 79, 063631 (2009)]. In the same apparatus we also achieve condensation in an optically plugged quadrupole trap [K. B. Davis et al., Phys. Rev. Lett. 75, 3969 (1995)] and show that as little as 70 mW of plug-laser power is sufficient for condensation, making it viable to pursue this approach using inexpensive diode lasers. While very compact, our apparatus features sufficient optical access for complex experiments, and we have recently used it to demonstrate condensation in a uniform optical-box potential [A. Gaunt et al., arXiv:1212.4453 (2012)].