Tobias Donner

Cavity Optomechanics with a Bose-Einstein Condensate

Cavity optomechanics studies the coupling between a mechanical oscillator and the electromagnetic field in a cavity. We report on a cavity optomechanical system in which a collective density excitation of a Bose-Einstein condensate serves as the mechanical oscillator coupled to the cavity field. A few photons inside the ultrahigh-finesse cavity trigger strongly driven back-action dynamics, in quantitative agreement with a cavity optomechanical model. We approach the strong coupling regime of cavity optomechanics, where a single excitation of the mechanical oscillator substantially influences the cavity field. The results open up new directions for investigating mechanical oscillators in the quantum regime and the border between classical and quantum physics.

Cavity QED with a Bose-Einstein condensate.

Cavity quantum electrodynamics (cavity QED) describes the coherent interaction between matter and an electromagnetic field confined within a resonator structure, and is providing a useful platform for developing concepts in quantum information processing. By using high-quality resonators, a strong coupling regime can be reached experimentally in which atoms coherently exchange a photon with a single light-field mode many times before dissipation sets in. This has led to fundamental studies with both microwave and optical resonators. To meet the challenges posed by quantum state engineering and quantum information processing, recent experiments have focused on laser cooling and trapping of atoms inside an optical cavity. However, the tremendous degree of control over atomic gases achieved with Bose–Einstein condensation has so far not been used for cavity QED. Here we achieve the strong coupling of a Bose–Einstein condensate to the quantized field of an ultrahigh-finesse optical cavity and present a measurement of its eigenenergy spectrum. This is a conceptually new regime of cavity QED, in which all atoms occupy a single mode of a matter-wave field and couple identically to the light field, sharing a single excitation. This opens possibilities ranging from quantum communication to a wealth of new phenomena that can be expected in the many-body physics of quantum gases with cavity-mediated interactions.

Quantum phases from competing short- and long-range interactions in an optical lattice

Insights into complex phenomena in quantum matter can be gained from simulation experiments with ultracold atoms, especially in cases where theoretical characterization is challenging. However, these experiments are mostly limited to short-range collisional interactions; recently observed perturbative effects of long-range interactions were too weak to reach new quantum phases. Here we experimentally realize a bosonic lattice model with competing short- and long-range interactions, and observe the appearance of four distinct quantum phases—a superfluid, a supersolid, a Mott insulator and a charge density wave. Our system is based on an atomic quantum gas trapped in an optical lattice inside a high-finesse optical cavity. The strength of the short-range on-site interactions is controlled by means of the optical lattice depth. The long (infinite)-range interaction potential is mediated by a vacuum mode of the cavity and is independently controlled by tuning the cavity resonance. When probing the phase transition between the Mott insulator and the charge density wave in real time, we observed a behaviour characteristic of a first-order phase transition. Our measurements have accessed a regime for quantum simulation of many-body systems where the physics is determined by the intricate competition between two different types of interactions and the zero point motion of the particles.

Roton-type mode softening in a quantum gas with cavity-mediated long-range interactions.

Cavity-Induced Minimum Tuning the strength and range of interactions in cold atomic gases is crucial to their role as quantum simulators. Most atom-atom interactions are short-ranged. One way to extend the range is to couple the gas to an optical cavity, which can propagate interactions between atoms, making the interactions effectively long-ranged. This system has been used to observe a transition to a “supersolid” phase characterized by a checkerboard atomic density order. Mottl et al. (p. 1570, published online 17 May) used Bragg spectroscopy to measure the excitation spectrum of an ultracold gas of Rb-87 atoms as the interaction strength was varied. Consistent with theoretical predictions, a minimum was observed in the excitation energy, similar to that observed in roton excitations of the superfluid helium. Low-energy excitations of the type present in superfluid helium are observed in a cold gas of rubidium atoms. Long-range interactions in quantum gases are predicted to give rise to an excitation spectrum of roton character, similar to that observed in superfluid helium. We investigated the excitation spectrum of a Bose-Einstein condensate with cavity-mediated long-range interactions, which couple all particles to each other. Increasing the strength of the interaction leads to a softening of an excitation mode at a finite momentum, preceding a superfluid-to-supersolid phase transition. We used a variant of Bragg spectroscopy to study the mode softening across the phase transition. The measured spectrum was in very good agreement with ab initio calculations and, at the phase transition, a diverging susceptibility was observed. The work paves the way toward quantum simulation of long-range interacting many-body systems.

Critical Behavior of a Trapped Interacting Bose Gas

The phase transition of Bose-Einstein condensation was studied in the critical regime, where fluctuations extend far beyond the length scale of thermal de Broglie waves. We used matter-wave interference to measure the correlation length of these critical fluctuations as a function of temperature. Observations of the diverging behavior of the correlation length above the critical temperature enabled us to determine the critical exponent of the correlation length for a trapped, weakly interacting Bose gas to be ν = 0.67 ± 0.13. This measurement has direct implications for the understanding of second-order phase transitions.

Observing the formation of long-range order during Bose-Einstein condensation.

We have experimentally investigated the formation of off-diagonal long-range order in a gas of ultracold atoms. A magnetically trapped atomic cloud prepared in a highly nonequilibrium state thermalizes and thereby crosses the Bose-Einstein condensation phase transition. The evolution of phase coherence between different regions of the sample is constantly monitored and information on the spatial first-order correlation function is obtained. We observe the growth of the spatial coherence and the formation of long-range order in real time and compare it to the growth of the atomic density. Moreover, we study the evolution of the momentum distribution during the nonequilibrium formation of the condensate.

Real-time observation of fluctuations at the driven-dissipative Dicke phase transition

We experimentally study the influence of dissipation on the driven Dicke quantum phase transition, realized by coupling external degrees of freedom of a Bose–Einstein condensate to the light field of a high-finesse optical cavity. The cavity provides a natural dissipation channel, which gives rise to vacuum-induced fluctuations and allows us to observe density fluctuations of the gas in real-time. We monitor the divergence of these fluctuations over two orders of magnitude while approaching the phase transition, and observe a behavior that deviates significantly from that expected for a closed system. A correlation analysis of the fluctuations reveals the diverging time scale of the atomic dynamics and allows us to extract a damping rate for the external degree of freedom of the atoms. We find good agreement with our theoretical model including dissipation via both the cavity field and the atomic field. Using a dissipation channel to nondestructively gain information about a quantum many-body system provides a unique path to study the physics of driven-dissipative systems.

Cavity QED detection of interfering matter waves

We observe the build-up of a matter wave interference pattern from single atom detection events in a double-slit experiment. The interference arises from two overlapping atom laser beams extracted from a rubidium Bose-Einstein condensate. Our detector is a high-finesse optical cavity which realizes a quantum measurement of the presence of an atom and thereby projects delocalized atoms into a state with zero or one atom in the resonator. The experiment reveals simultaneously the granular and the wave nature of matter. We present a setup which is suited for applications in atom interferometry and cavity QED.

Phase Transitions in a Bose-Hubbard Model with Cavity-Mediated Global-Range Interactions

We study a system with competing short- and global-range interactions in the framework of the Bose-Hubbard model. Using a mean-field approximation we obtain the phase diagram of the system and observe four different phases: a superfluid, a supersolid, a Mott insulator and a charge density wave, where the transitions between the various phases can be either of first or second order. We qualitatively support these results using Monte-Carlo simulations. An analysis of the low-energy excitations shows that the second-order phase transition from the charge density wave to the supersolid is associated with the softening of particle- and hole-like excitations which give rise to a gapless mode and an amplitude Higgs mode in the supersolid phase. This amplitude Higgs mode is further transformed into a roton mode which softens at the supersolid to superfluid phase transition.

Metastability and avalanche dynamics in strongly correlated gases with long-range interactions

Significance Most structured matter, whether in the form of solids or macromolecules, is found in metastable states. Metastability, as well as the transition processes between metastable states, is ubiquitous in nature, but challenges our tools to describe such complex quantum systems. Using a quantum gas, we assemble a synthetic quantum many-body system featuring metastability. The essential ingredient is a global interaction that couples superfluid shells of the system with a metastable Mott insulator in its core. We study in real time the self-induced switching of the core to a different density configuration, a process reminiscent of the folding between discrete structures encountered in the study of macromolecules. We experimentally study the stability of a bosonic Mott insulator against the formation of a density wave induced by long-range interactions and characterize the intrinsic dynamics between these two states. The Mott insulator is created in a quantum degenerate gas of 87-Rubidium atoms, trapped in a 3D optical lattice. The gas is located inside and globally coupled to an optical cavity. This causes interactions of global range, mediated by photons dispersively scattered between a transverse lattice and the cavity. The scattering comes with an atomic density modulation, which is measured by the photon flux leaking from the cavity. We initialize the system in a Mott-insulating state and then rapidly increase the global coupling strength. We observe that the system falls into either of two distinct final states. One is characterized by a low photon flux, signaling a Mott insulator, and the other is characterized by a high photon flux, which we associate with a density wave. Ramping the global coupling slowly, we observe a hysteresis loop between the two states—a further signature of metastability. A comparison with a theoretical model confirms that the metastability originates in the competition between short- and global-range interactions. From the increasing photon flux monitored during the switching process, we find that several thousand atoms tunnel to a neighboring site on the timescale of the single-particle dynamics. We argue that a density modulation, initially forming in the compressible surface of the trapped gas, triggers an avalanche tunneling process in the Mott-insulating region.