Observation of the Fermionic Joule-Thomson Effect.

We report the first observation of the quantum Joule-Thomson (JT) effect in ideal and unitary Fermi gases. We study the temperature dynamics of these systems while they undergo an energy-per-particle conserving rarefaction. For scale-invariant systems, whose equations of state satisfy the relation U∝PV, this rarefaction conserves the specific enthalpy, which makes it thermodynamically equivalent to a JT throttling process. We observe JT heating in an ideal Fermi gas, a direct consequence of Pauli blocking. In a unitary Fermi gas, we observe that the JT heating is marginal in the temperature range 0.2≲T/T_{F}≲0.8 as the repulsive quantum-statistical effect is lessened by the attractive interparticle interactions.

Stability of the Repulsive Fermi Gas with Contact Interactions.

We report the creation and the study of the stability of a repulsive quasihomogeneous spin-1/2 Fermi gas with contact interactions. For the range of scattering lengths a explored, the dominant mechanism of decay is a universal three-body recombination toward a Feshbach bound state. We observe that the recombination coefficient K_{3}∝ε_{kin}a^{6}, where the first factor, the average kinetic energy per particle ε_{kin}, arises from a three-body threshold law, and the second one from the universality of recombination. Both scaling laws are consequences of Pauli blocking effects in three-body collisions involving two identical fermions. As a result of the interplay between Fermi statistics and the momentum dependence of the recombination process, the system exhibits nontrivial temperature dynamics during recombination, alternatively heating or cooling depending on its initial quantum degeneracy. The measurement of K_{3} provides an upper bound for the interaction strength achievable in equilibrium for a uniform repulsive Fermi gas.

Emergence of a turbulent cascade in a quantum gas.

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.

Many-Body Decay of the Gapped Lowest Excitation of a Bose-Einstein Condensate.

We study the decay mechanism of the gapped lowest-lying axial excitation of a quasipure atomic Bose-Einstein condensate confined in a cylindrical box trap. Owing to the absence of accessible lower-energy modes, or direct coupling to an external bath, this excitation is protected against one-body (linear) decay, and the damping mechanism is exclusively nonlinear. We develop a universal theoretical model that explains this fundamentally nonlinear damping as a process whereby two quanta of the gapped lowest excitation mode couple to a higher-energy mode, which subsequently decays into a continuum. We find quantitative agreement between our experiments and the predictions of this model. Finally, by strongly driving the system below its (lowest) resonant frequency, we observe third-harmonic generation, a hallmark of nonlinear behavior.

Measurement of the magnetic interaction between two bound electrons of two separate ions.

Electrons have an intrinsic, indivisible, magnetic dipole aligned with their internal angular momentum (spin). The magnetic interaction between two electronic spins can therefore impose a change in their orientation. Similar dipolar magnetic interactions exist between other spin systems and have been studied experimentally. Examples include the interaction between an electron and its nucleus and the interaction between several multi-electron spin complexes. The challenge in observing such interactions for two electrons is twofold. First, at the atomic scale, where the coupling is relatively large, it is often dominated by the much larger Coulomb exchange counterpart. Second, on scales that are substantially larger than the atomic, the magnetic coupling is very weak and can be well below the ambient magnetic noise. Here we report the measurement of the magnetic interaction between the two ground-state spin-1/2 valence electrons of two (88)Sr(+) ions, co-trapped in an electric Paul trap. We varied the ion separation, d, between 2.18 and 2.76 micrometres and measured the electrons' weak, millihertz-scale, magnetic interaction as a function of distance, in the presence of magnetic noise that was six orders of magnitude larger than the magnetic fields the electrons apply on each other. The cooperative spin dynamics was kept coherent for 15 seconds, during which spin entanglement was generated, as verified by a negative measured value of -0.16 for the swap entanglement witness. The sensitivity necessary for this measurement was provided by restricting the spin evolution to a decoherence-free subspace that is immune to collective magnetic field noise. Our measurements show a d(-3.0(4)) distance dependence for the coupling, consistent with the inverse-cube law.

Quantum Depletion of a Homogeneous Bose-Einstein Condensate.

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.

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

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.

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

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.

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

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.

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.

Addressing two-level systems variably coupled to an oscillating field.

We propose a simple method to spectrally resolve an array of identical two-level systems coupled to an inhomogeneous oscillating field. The addressing protocol uses a dressing field with a spatially dependent coupling to the atoms. We validate this scheme experimentally by realizing single-spin addressing of a linear chain of trapped ions that are separated by ~3 µm, dressed by a laser field that is resonant with the micromotion sideband of a narrow optical transition.

Stability of a unitary Bose gas.

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.

Dynamics and thermodynamics of the low-temperature strongly interacting Bose gas.

We measure the zero-temperature equation of state of a homogeneous Bose gas of (7)Li atoms by analyzing the in situ density distributions of trapped samples. For increasing repulsive interactions our data show a clear departure from mean-field theory and provide a quantitative test of the many-body corrections first predicted in 1957 by Lee, Huang, and Yang [Phys. Rev. 106, 1135 (1957).]. We further probe the dynamic response of the Bose gas to a varying interaction strength and compare it to simple theoretical models. We deduce a lower bound for the value of the universal constant ξ > 0.44(8) that would characterize the universal Bose gas at the unitary limit.

Synthetic dissipation and cascade fluxes in a turbulent quantum gas.

Scale-invariant fluxes are the defining property of turbulent cascades, but their direct measurement is a challenging experimental problem. Here we perform such a measurement for a direct energy cascade in a turbulent quantum gas. Using a time-periodic force, we inject energy at a large length scale and generate a cascade in a uniformly trapped three-dimensional Bose gas. The adjustable trap depth provides a high-momentum cutoff k D, which realizes a synthetic dissipation scale. This gives us direct access to the particle flux across a momentum shell of radius k D, and the tunability of k D allows for a clear demonstration of the zeroth law of turbulence. Moreover, our time-resolved measurements give unique access to the pre-steady-state dynamics, when the cascade front propagates in momentum space.

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

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.

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

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.