Ferdinand Brennecke

Dicke quantum phase transition with a superfluid gas in an optical cavity

A phase transition describes the sudden change of state of a physical system, such as melting or freezing. Quantum gases provide the opportunity to establish a direct link between experiments and generic models that capture the underlying physics. The Dicke model describes a collective matter–light interaction and has been predicted to show an intriguing quantum phase transition. Here we realize the Dicke quantum phase transition in an open system formed by a Bose–Einstein condensate coupled to an optical cavity, and observe the emergence of a self-organized supersolid phase. The phase transition is driven by infinitely long-range interactions between the condensed atoms, induced by two-photon processes involving the cavity mode and a pump field. We show that the phase transition is described by the Dicke Hamiltonian, including counter-rotating coupling terms, and that the supersolid phase is associated with a spontaneously broken spatial symmetry. The boundary of the phase transition is mapped out in quantitative agreement with the Dicke model. Our results should facilitate studies of quantum gases with long-range interactions and provide access to novel quantum phases.

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.

Cold atoms in cavity-generated dynamical optical potentials

We review state-of-the-art theory and experiment of the motion of cold and ultracold atoms coupled to the radiation field within a high-finesse optical resonator in the dispersive regime of the atom-field interaction with small internal excitation. The optical dipole force on the atoms together with the back-action of atomic motion onto the light field gives rise to a complex nonlinear coupled dynamics. As the resonator constitutes an open driven and damped system, the dynamics is non-conservative and in general enables cooling and confining the motion of polarizable particles. In addition, the emitted cavity field allows for real-time monitoring of the particles position with minimal perturbation up to sub-wavelength accuracy. For many-body systems, the resonator field mediates controllable long-range atom-atom interactions, which set the stage for collective phenomena. Besides correlated motion of distant particles, one finds critical behavior and non-equilibrium phase transitions between states of different atomic order in conjunction with superradiant light scattering. Quantum degenerate gases inside optical resonators can be used to emulate opto-mechanics as well as novel quantum phases like supersolids and spin glasses. Non-equilibrium quantum phase transitions, as predicted by e.g. the Dicke Hamiltonian, can be controlled and explored in real-time via monitoring the cavity field. In combination with optical lattices, the cavity field can be utilized for non-destructive probing Hubbard physics and tailoring long-range interactions for ultracold quantum systems.

Exploring Symmetry Breaking at the Dicke Quantum Phase Transition

We study symmetry breaking at the Dicke quantum phase transition by coupling a motional degree of freedom of a Bose-Einstein condensate to the field of an optical cavity. Using an optical heterodyne detection scheme, we observe symmetry breaking in real time and distinguish the two superradiant phases. We explore the process of symmetry breaking in the presence of a small symmetry-breaking field and study its dependence on the rate at which the critical point is crossed. Coherent switching between the two ordered phases is demonstrated.

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.

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.

Removal of violations of the Master Ward Identity in perturbative QFT

We study the appearance of anomalies of the Master Ward Identity, which is a universal renormalization condition in perturbative QFT. The main insight of the present paper is that any violation of the Master Ward Identity can be expressed as a local interacting field; this is a version of the well-known Quantum Action Principle of Lowenstein and Lam. Proceeding in a proper field formalism by induction on the order in ħ, this knowledge about the structure of possible anomalies as well as techniques of algebraic renormalization are used to remove possible anomalies by finite renormalizations. As an example, the method is applied to prove the Ward identities of the O(N) scalar field model.

Dynamical coupling between a Bose–Einstein condensate and a cavity optical lattice

A Bose–Einstein condensate is dispersively coupled to a single mode of an ultra-high finesse optical cavity. The system is governed by strong interactions between the atomic motion and the light field even at the level of single quanta. While coherently pumping the cavity mode the condensate is subject to the cavity optical lattice potential whose depth depends nonlinearly on the atomic density distribution. We observe optical bistability already below the single photon level and strong back-action dynamics which tunes the coupled system periodically out of resonance.

Measuring the dynamic structure factor of a quantum gas undergoing a structural phase transition

The dynamic structure factor is a central quantity describing the physics of quantum many-body systems, capturing structure and collective excitations of a material. In condensed matter, it can be measured via inelastic neutron scattering, which is an energy-resolving probe for the density fluctuations. In ultracold atoms, a similar approach could so far not be applied because of the diluteness of the system. Here we report on a direct, real-time and nondestructive measurement of the dynamic structure factor of a quantum gas exhibiting cavity-mediated long-range interactions. The technique relies on inelastic scattering of photons, stimulated by the enhanced vacuum field inside a high finesse optical cavity. We extract the density fluctuations, their energy and lifetime while the system undergoes a structural phase transition. We observe an occupation of the relevant quasi-particle mode on the level of a few excitations, and provide a theoretical description of this dissipative quantum many-body system.