Two-Particle Interference with Double Twin-Atom Beams.

We demonstrate a source for correlated pairs of atoms characterized by two opposite momenta and two spatial modes forming a Bell state only involving external degrees of freedom. We characterize the state of the emitted atom beams by observing strong number squeezing up to -10 dB in the correlated two-particle modes of emission. We furthermore demonstrate genuine two-particle interference in the normalized second-order correlation function g^{(2)} relative to the emitted atoms.

Ergodic-Localized Junctions in a Periodically Driven Spin Chain.

We report the analog simulation of an ergodic-localized junction by using an array of 12 coupled superconducting qubits. To perform the simulation, we fabricated a superconducting quantum processor that is divided into two domains: one is a driven domain representing an ergodic system, while the second is localized under the effect of disorder. Because of the overlap between localized and delocalized states, for a small disorder there is a proximity effect and localization is destroyed. To experimentally investigate this, we prepare a microwave excitation in the driven domain and explore how deep it can penetrate the disordered region by probing its dynamics. Furthermore, we perform an ensemble average over 50 realizations of disorder, which clearly shows the proximity effect. Our work opens a new avenue to build quantum simulators of driven-disordered systems with applications in condensed matter physics and material science.

Solid-state electron spin lifetime limited by phononic vacuum modes.

Longitudinal relaxation is the process by which an excited spin ensemble decays into its thermal equilibrium with the environment. In solid-state spin systems, relaxation into the phonon bath usually dominates over the coupling to the electromagnetic vacuum1-9. In the quantum limit, the spin lifetime is determined by phononic vacuum fluctuations 10 . However, this limit was not observed in previous studies due to thermal phonon contributions11-13 or phonon-bottleneck processes10, 14,15. Here we use a dispersive detection scheme16,17 based on cavity quantum electrodynamics18-21 to observe this quantum limit of spin relaxation of the negatively charged nitrogen vacancy (NV-) centre 22 in diamond. Diamond possesses high thermal conductivity even at low temperatures 23 , which eliminates phonon-bottleneck processes. We observe exceptionally long longitudinal relaxation times T1 of up to 8 h. To understand the fundamental mechanism of spin-phonon coupling in this system we develop a theoretical model and calculate the relaxation time ab initio. The calculations confirm that the low phononic density of states at the NV- transition frequency enables the spin polarization to survive over macroscopic timescales.

Coherent Coupling of Remote Spin Ensembles via a Cavity Bus.

We report coherent coupling between two macroscopically separated nitrogen-vacancy electron spin ensembles in a cavity quantum electrodynamics system. The coherent interaction between the distant ensembles is directly detected in the cavity transmission spectrum by observing bright and dark collective multiensemble states and an increase of the coupling strength to the cavity mode. Additionally, in the dispersive limit we show transverse ensemble-ensemble coupling via virtual photons.

Cooling of a One-Dimensional Bose Gas.

We experimentally study the dynamics of a degenerate one-dimensional Bose gas that is subject to a continuous outcoupling of atoms. Although standard evaporative cooling is rendered ineffective by the absence of thermalizing collisions in this system, we observe substantial cooling. This cooling proceeds through homogeneous particle dissipation and many-body dephasing, enabling the preparation of otherwise unexpectedly low temperatures. Our observations establish a scaling relation between temperature and particle number, and provide insights into equilibration in the quantum world.

Implementation of the Dicke lattice model in hybrid quantum system arrays.

Generalized Dicke models can be implemented in hybrid quantum systems built from ensembles of nitrogen-vacancy (NV) centers in diamond coupled to superconducting microwave cavities. By engineering cavity assisted Raman transitions between two spin states of the NV defect, a fully tunable model for collective light-matter interactions in the ultrastrong coupling limit can be obtained. Our analysis of the resulting nonequilibrium phases for a single cavity and for coupled cavity arrays shows that different superradiant phase transitions can be observed using existing experimental technologies, even in the presence of large inhomogeneous broadening of the spin ensemble. The phase diagram of the Dicke lattice model displays distinct features induced by dissipation, which can serve as a genuine experimental signature for phase transitions in driven open quantum systems.

Multimode dynamics and emergence of a characteristic length scale in a one-dimensional quantum system.

We study the nonequilibrium dynamics of a coherently split one-dimensional Bose gas by measuring the full probability distribution functions of matter-wave interference. Observing the system on different length scales allows us to probe the dynamics of excitations on different energy scales, revealing two distinct length-scale-dependent regimes of relaxation. We measure the crossover length scale separating these two regimes and identify it with the prethermalized phase-correlation length of the system. Our approach enables a direct observation of the multimode dynamics characterizing one-dimensional quantum systems.

Non-equilibrium coherence dynamics in one-dimensional Bose gases.

Low-dimensional systems provide beautiful examples of many-body quantum physics. For one-dimensional (1D) systems, the Luttinger liquid approach provides insight into universal properties. Much is known of the equilibrium state, both in the weakly and strongly interacting regimes. However, it remains a challenge to probe the dynamics by which this equilibrium state is reached. Here we present a direct experimental study of the coherence dynamics in both isolated and coupled degenerate 1D Bose gases. Dynamic splitting is used to create two 1D systems in a phase coherent state. The time evolution of the coherence is revealed through local phase shifts of the subsequently observed interference patterns. Completely isolated 1D Bose gases are observed to exhibit universal sub-exponential coherence decay, in excellent agreement with recent predictions. For two coupled 1D Bose gases, the coherence factor is observed to approach a non-zero equilibrium value, as predicted by a Bogoliubov approach. This coupled-system decay to finite coherence is the matter wave equivalent of phase-locking two lasers by injection. The non-equilibrium dynamics of superfluids has an important role in a wide range of physical systems, such as superconductors, quantum Hall systems, superfluid helium and spin systems. Our experiments studying coherence dynamics show that 1D Bose gases are ideally suited for investigating this class of phenomena.

Two-point phase correlations of a one-dimensional bosonic Josephson junction.

We realize a one-dimensional Josephson junction using quantum degenerate Bose gases in a tunable double well potential on an atom chip. Matter wave interferometry gives direct access to the relative phase field, which reflects the interplay of thermally driven fluctuations and phase locking due to tunneling. The thermal equilibrium state is characterized by probing the full statistical distribution function of the two-point phase correlation. Comparison to a stochastic model allows us to measure the coupling strength and temperature and hence a full characterization of the system.

Cavity QED with magnetically coupled collective spin states.

We report strong coupling between an ensemble of nitrogen-vacancy center electron spins in diamond and a superconducting microwave coplanar waveguide resonator. The characteristic scaling of the collective coupling strength with the square root of the number of emitters is observed directly. Additionally, we measure hyperfine coupling to (13)C nuclear spins, which is a first step towards a nuclear ensemble quantum memory. Using the dispersive shift of the cavity resonance frequency, we measure the relaxation time of the NV center at millikelvin temperatures in a nondestructive way.

Weakly interacting Bose gas in the one-dimensional limit.

We prepare a chemically and thermally one-dimensional (1D) quantum degenerate Bose gas in a single microtrap. We introduce a new interferometric method to distinguish the quasicondensate fraction of the gas from the thermal cloud at finite temperature. We reach temperatures down to kT≈0.5ℏω(⊥) (transverse oscillator eigenfrequency ω(⊥)) when collisional thermalization slows down as expected in 1D. At the lowest temperatures the transverse-momentum distribution exhibits a residual dependence on the line density n(1D), characteristic for 1D systems. For very low densities the approach to the transverse single-particle ground state is linear in n(1D).

Fluctuations and stochastic processes in one-dimensional many-body quantum systems.

We study the fluctuation properties of a one-dimensional many-body quantum system composed of interacting bosons and investigate the regimes where quantum noise or, respectively, thermal excitations are dominant. For the latter, we develop a semiclassical description of the fluctuation properties based on the Ornstein-Uhlenbeck stochastic process. As an illustration, we analyze the phase correlation functions and the full statistical distributions of the interference between two one-dimensional systems, either independent or tunnel-coupled, and compare with the Luttinger-liquid theory.

Optical lattice on an atom chip.

Optical dipole traps and atom chips are two very powerful tools for the quantum manipulation of neutral atoms. We demonstrate that both methods can be combined by creating an optical lattice potential on an atom chip. A red-detuned laser beam is retroreflected using the atom chip surface as a high-quality mirror, generating a vertical array of purely optical oblate traps. We transfer thermal atoms from the chip into the lattice and observe cooling into the two-dimensional regime. Using a chip-generated Bose-Einstein condensate, we demonstrate coherent Bloch oscillations in the lattice.

Optimal control of complex atomic quantum systems.

Quantum technologies will ultimately require manipulating many-body quantum systems with high precision. Cold atom experiments represent a stepping stone in that direction: a high degree of control has been achieved on systems of increasing complexity. However, this control is still sub-optimal. In many scenarios, achieving a fast transformation is crucial to fight against decoherence and imperfection effects. Optimal control theory is believed to be the ideal candidate to bridge the gap between early stage proof-of-principle demonstrations and experimental protocols suitable for practical applications. Indeed, it can engineer protocols at the quantum speed limit - the fastest achievable timescale of the transformation. Here, we demonstrate such potential by computing theoretically and verifying experimentally the optimal transformations in two very different interacting systems: the coherent manipulation of motional states of an atomic Bose-Einstein condensate and the crossing of a quantum phase transition in small systems of cold atoms in optical lattices. We also show that such processes are robust with respect to perturbations, including temperature and atom number fluctuations.

Non-equilibrium scale invariance and shortcuts to adiabaticity in a one-dimensional Bose gas.

We present experimental evidence for scale invariant behaviour of the excitation spectrum in phase-fluctuating quasi-1d Bose gases after a rapid change of the external trapping potential. Probing density correlations in free expansion, we find that the temperature of an initial thermal state scales with the spatial extension of the cloud as predicted by a model based on adiabatic rescaling of initial eigenmodes with conserved quasiparticle occupation numbers. Based on this result, we demonstrate that shortcuts to adiabaticity for the rapid expansion or compression of the gas do not induce additional heating.

Towards experimental quantum-field tomography with ultracold atoms.

The experimental realization of large-scale many-body systems in atomic-optical architectures has seen immense progress in recent years, rendering full tomography tools for state identification inefficient, especially for continuous systems. To work with these emerging physical platforms, new technologies for state identification are required. Here we present first steps towards efficient experimental quantum-field tomography. Our procedure is based on the continuous analogues of matrix-product states, ubiquitous in condensed-matter theory. These states naturally incorporate the locality present in realistic physical settings and are thus prime candidates for describing the physics of locally interacting quantum fields. To experimentally demonstrate the power of our procedure, we quench a one-dimensional Bose gas by a transversal split and use our method for a partial quantum-field reconstruction of the far-from-equilibrium states of this system. We expect our technique to play an important role in future studies of continuous quantum many-body systems.

Controlling cold atoms using nanofabricated surfaces: atom chips

Atoms can be trapped and guided using nanofabricated wires on surfaces, achieving the scales required by quantum information proposals. These atom chips form the basis for robust and widespread applications of cold atoms ranging from atom optics to fundamental questions in mesoscopic physics, and possibly quantum information systems.

Interferometry with non-classical motional states of a Bose-Einstein condensate.

The Ramsey interferometer is a prime example of precise control at the quantum level. It is usually implemented using internal states of atoms, molecules or ions, for which powerful manipulation procedures are now available. Whether it is possible to control external degrees of freedom of more complex, interacting many-body systems at this level remained an open question. Here we demonstrate a two-pulse Ramsey-type interferometer for non-classical motional states of a Bose-Einstein condensate in an anharmonic trap. The control sequences used to manipulate the condensate wavefunction are obtained from optimal control theory and are directly optimized to maximize the interferometric contrast. They permit a fast manipulation of the atomic ensemble compared to the intrinsic decay processes and many-body dephasing effects. This allows us to reach an interferometric contrast of 92% in the experimental implementation.

Integrated Mach-Zehnder interferometer for Bose-Einstein condensates.

Particle-wave duality enables the construction of interferometers for matter waves, which complement optical interferometers in precision measurement devices. This requires the development of atom-optics analogues to beam splitters, phase shifters and recombiners. Integrating these elements into a single device has been a long-standing goal. Here we demonstrate a full Mach-Zehnder sequence with trapped Bose-Einstein condensates confined on an atom chip. Particle interactions in our Bose-Einstein condensate matter waves lead to a nonlinearity, absent in photon optics. We exploit it to generate a non-classical state having reduced number fluctuations inside the interferometer. Making use of spatially separated wave packets, a controlled phase shift is applied and read out by a non-adiabatic matter-wave recombiner. We demonstrate coherence times a factor of three beyond what is expected for coherent states, highlighting the potential of entanglement as a resource for metrology. Our results pave the way for integrated quantum-enhanced matter-wave sensors.

Relaxation and prethermalization in an isolated quantum system.

Understanding relaxation processes is an important unsolved problem in many areas of physics. A key challenge is the scarcity of experimental tools for the characterization of complex transient states. We used measurements of full quantum mechanical probability distributions of matter-wave interference to study the relaxation dynamics of a coherently split one-dimensional Bose gas and obtained comprehensive information about the dynamical states of the system. After an initial rapid evolution, the full distributions reveal the approach toward a thermal-like steady state characterized by an effective temperature that is independent from the initial equilibrium temperature of the system before the splitting process. We conjecture that this state can be described through a generalized Gibbs ensemble and associate it with prethermalization.