# Cavity quantum electrodynamics with ultracold gases

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Our cavity experiment bridges two central research fields in quantum optics and atomic physics: ultracold quantum gases and cavity quantum electrodynamics (QED). Combining these two research fields opens access to a fascinating area of quantum systems where both light and matter act as dynamical and strongly coupled degrees of freedom.

In our setup we routinely prepare Bose-Einstein condensates of Rb 87 in the close vicinity or inside the field of an ultrahigh-finesse optical cavity with small mode volume. The system is capable to reach the strong coupling regime where single atoms and single photons interact on a timescale faster than any decay processes. This allows us to use the cavity as a sensitive detector of single atoms which are coherently extracted from a Bose-Einstein condensate in order to gain insight into the physics of Bose-Einstein condensation. In the dispersive regime the system is governed by the retroaction of the collective atomic motion of the Bose-Einstein condensate upon the cavity light field, and by atomic long-range interactions which are mediated by the cavity field.

## Continuous feedback on a quantum gas coupled to an optical cavity

### 05 December 2019

We present an active feedback scheme acting continuously on the state of a quantum gas dispersively coupled to a high-finesse optical cavity. The quantum gas is subject to a transverse pump laser field inducing a self-organization phase transition, where the gas acquires a density modulation and photons are scattered into the resonator. Photons leaking from the cavity allow for a real-time and non-destructive readout of the system. We stabilize the mean intra-cavity photon number through a micro-processor controlled feedback architecture acting on the intensity of the transverse pump field. The feedback scheme can keep the mean intra-cavity photon number nph constant, in a range between nph=0.17Â±0.04 and nph=27.6Â±0.5, and for up to 4 s. Thus we can engage the stabilization in a regime where the system is very close to criticality as well as deep in the self-organized phase. The presented scheme allows us to approach the self-organization phase transition in a highly controlled manner and is a first step on the path towards the realization of many-body phases driven by tailored feedback mechanisms.

Read the preprint: arXiv:1912.02505

## Dissipation Induced Structural Instability and Chiral Dynamics in a Quantum Gas

### 17 January 2019

Dissipative and unitary processes define the evolution of a many-body system. Their interplay gives rise to dynamical phase transitions and can lead to instabilities. We discovered a non-stationary state of chiral nature in a synthetic many-body system with independently controllable unitary and dissipative couplings. Our experiment is based on a spinor Bose gas interacting with an optical resonator. Orthogonal quadratures of the resonator field coherently couple the Bose-Einstein condensate to two different atomic spatial modes whereas the dispersive effect of the resonator losses mediates a dissipative coupling between these modes. In a regime of dominant dissipative coupling we observe the chiral evolution and map it to a positional instability.

Read the ETHZ press release: Unexpected twist in a quantum system

Read the paper: Science 366, 1496-1499 (2019)

Read the preprint: arXiv:1901.05974

## Formation of a Spin Texture in a Quantum Gas Coupled to a Cavity

### 31 May 2018

We observe cavity mediated spin-dependent interactions in an off-resonantly driven multilevel atomic Bose-Einstein condensate that is strongly coupled to an optical cavity. Applying a driving field with adjustable polarization, we identify the roles of the scalar and the vectorial components of the atomic polarizability tensor for single and multicomponent condensates. Beyond a critical strength of the vectorial coupling, we infer the formation of a spin texture in a condensate of two internal states from the analysis of the cavity output field. Our work provides perspectives for global dynamical gauge fields and self-consistently spin-orbit coupled gases.

Read the paper on PRL 120, 223602

Read the preprint: arXiv:1803.01803

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

### 27 March 2018

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.

Read the paper: PNAS March 27, 2018 115 (13)

Read the preprint: arXiv:1708.02229

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

### 7 May 2016

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 novel quantum phases. Here we experimentally realize a bosonic lattice model with competing short- and infinite-range interactions, and observe the appearance of four distinct 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-ranged on-site interactions is controlled by means of the optical lattice depth. The 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 discovered 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.

Read the paper on Nature 532, 476-479 (2016)

Read the preprint: arXiv:1511.00007

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

### 6 May 2015

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.

Read the paper: Nature Communications 6, 7046 (2015)

Read the preprint: arXiv:1503.05565

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

### 15 May 2013

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 which significantly deviates 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 both dissipation via the cavity field and via the atomic field. Utilizing a dissipation channel to non-destructively gain information about a quantum many-body system provides a unique path to study the physics of driven-dissipative systems.

Read the paper on PNAS 110, 11763-11767 (2013)

Read the preprint: arXiv:1304.4939

## Observation of roton-type mode softening in a quantum gas with cavity-mediated long-range interactions

### 14 March 2012

Long-range interactions in quantum gases are predicted to give rise to a roton spectrum, as known from superfluid helium. We investigate 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. The mode softening is spectroscopically studied across the phase transition using a variant of Bragg spectroscopy. At the phase transition, a diverging susceptibility is observed. Very good agreement with ab initio calculations is found. The work paves the way towards quantum simulation of long-range interacting many-body systems.

Read the paper:Science 336, 1570 (2012)

Read the preprint: arXiv:1203.1322

## Exploring Symmetry Breaking at the Dicke Quantum Phase Transition

### 30 Sep 2011

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.

Read the paper: Phys. Rev. Lett. 107, 140402 (2011)

Read the preprint: arXiv:1105.0426

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

### 29 Apr 2010

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.

Read the paper: Nature 464, 1301 (2010)

Read the preprint: arXiv:0912.3261

## Cavity Optomechanics with a Bose-Einstein Condensate

### 10 October 2008

We realize 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.

Read the paper : Science 322, 235 (2008)

Read the preprint : arxiv:0807.2347

## Cavity QED with a Bose-Einstein Condensate

### 08 November 2007

We observe strong coupling between a Bose-Einstein condensate and the quantized light field in our high-finesse optical cavity. Because the atoms in the quantum degenerate gas occupy the same quantum state and are thus indistinguishable, we realize the Tavis-Cummings Hamiltonian, where all atoms have identical coupling to the light field.

As expected from the Tavis-Cummings model, the coupling strength scales with the square root of the atom number. Because of this enhancement, the coupling is so strong that we not only couple to the fundamental resonator mode, but also to higher order transverse modes of the cavity.

To produce a BEC in the mode of the optical resonator, we first prepare an ultra-cold cloud of atoms in the magnetic trap, 4cm above the cavity. We then load the atoms into a standing wave optical potential formed by two counter-propagating laser beams. By detuning the relative frequency between the two beams, the standing wave starts moving and we transport the atoms to the position of the cavity mode. There, the atoms are loaded into a crossed-beam dipole trap and are evaporatively cooled to quantum degeneracy.

Read the paper : Nature 450, 268 (2007)

Read the preprint: arXiv:0706.3411

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