# A versatile platform for atom-light interactions

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With this experiment, we explore and manipulate ultracold atoms in diverse self-generated, dynamical optical lattices provided by quantized light fields of several cavity modes. The dispersive coupling between cavity modes and quantum gases gives rise to photon-mediated interactions that can cause transitions to new quantum phases. Their static and dynamic properties can be investigated in real time in non-destructive ways by the light fields leaking from the cavities. This finite decay rate not only constitutes a powerful observable, but also alows to investigate the effect of dissipation in open systems onto quantum phases.

The experiment is designed in a modular way, that allows for rapid exchange of the cavity system. This enables us to explore a variety of different systems. Currently, a platform with two optical high-finesse cavities that cross under an angle of 60° is loaded into the vacuum chamber.

## First order phase transition between two centro-symmetric superradiant crystals

### 17 Apr 2020

We realized a synthetic crystal with two possible spatial configurations, formed by a quantum gas self-ordering within an optical cavity.
We demonstrate how these configurations are connected by a structural phase transition.
The transition is of first order and is accompanied by transient dynamics of the order parameter which we measure in real-time, showing interesting analogy to spontaneous crystal formation and electronic dynamics in real materials.
Our work relies on a novel experimental approach based on two unbalanced coupling beams. In addition, we proved that different structures arise even from a single mode cavity, as opposed to more complicated concepts based either on multimode cavities or multiple cavities.

Read the paper: PRR 3, L012024 (2021)

Read the preprint: arXiv:2004.08398

## P-band induced self-organization and dynamics with repulsively driven ultracoldatoms in an optical cavity

### 24 May 2019

We investigate a Bose-Einstein condensate strongly coupled to an optical cavity via a repulsive optical lattice. We detect a stable self-ordered phase in this regime, and show that the atoms order through an antisymmetric coupling to the P-band of the lattice, limiting the extent of the phase and changing the geometry of the emergent density modulation. Furthermore, we find a non-equilibrium phase with repeated intense bursts of the intra-cavity photon number, indicating non-trivial driven-dissipative dynamics.

Read the paper: PRL 123, 233601 (2019)

Read the preprint: arXiv:1905.10377

## Two-mode Dicke model from non-degenerate polarization modes

### 27 Feb 2019

We realise a two-mode Dicke model by coupling a BEC to the two fundamental polarisation modes of a single cavity,
to which we couple via both the scalar and vectorial polarisabilities of the atoms. By independently tuning the
relative interaction strengths, we determine the effect on the self-organisation phase transition, demonstrating a
crossover from a single-mode to a two-mode Dicke model.

Read the paper: PRA 100, 1 (2019)

Read the preprint: arxiv:1902.09831

## Coupling two order parameters in a quantum gas

### 17 Nov 2017

We use a quantum gas to engineer an adjustable interaction at the microscopic level between two orders, and demonstrate scenarios of competition,
coexistence and coupling between them. In the latter case, intriguingly, the presence of one order lowers the critical point of the other.
We characterize the intertwining between these orders by measuring the composite order parameter and the elementary excitations.
We explain our results with a mean-field free energy model, which is derived from a microscopic Hamiltonian.

Read the paper on Nature materials: DOI:10.1038/s41563-018-0118-1

Read the ETH article: "Putting a quantum gas through its phases".

Read the preprint: arxiv.org/abs/1711.07988

## Monitoring and manipulating Higgs and Goldstone modes

### 19 April 2017

We study the Higgs and Goldstone modes in a supersolid quantum gas that is created by coupling a Bose-Einstein condensate symmetrically to two optical cavities. The cavity fields form a U(1)-symmetric
order parameter that can be modulated and monitored along both quadratures in real time. This enables us to measure the excitation energies across the superfluid-supersolid phase transition, establish
their amplitude and phase nature, as well as characterize their dynamics from an impulse response. Furthermore, we can give a tunable mass to the Goldstone mode at the crossover between continuous and
discrete symmetry by changing the coupling of the quantum gas with either cavity.

Read the paper : Science, 358, 1415-1418

Read the ETH article: "Real-time observation of collective quantum modes".

Read the preprint: arxiv.org/abs/1704.05803

## Supersolid formation in a quantum gas

### 28 September 2016

We report on the crystallization of a superfluid quantum gas to a supersolid by breaking continuous translational symmetry. The control over the coupling strength between the atomic cloud and
two optical cavities allows us to tailor the cavity-mediated interactions between the atoms in such a way, that they give rise to a structural phase transition. The continuous symmetry breaking
finds its origin at the interplay of two discrete symmetries associated with a self-organisation phase transition to each cavity. We use the light fields leaking from the cavities to monitor the
position of the crystalline structure in real time, and to directly detect the ground state degeneracy of the supersolid.

Read the paper : Nature 543, 87 (2017)

Read the ETH article : "Can a solid be superfluid ?"

Read the News & Views by K. Hazzard : Nature 543, 47 (2017)

Read the preprint : arxiv:1609.09053

## Tuneable lens setup for transporting ultracold atoms

### 09 June 2014

We implemeted an optical setup with focus-tuneable lenses to dynamically control the waist and focus position of a laser beam, in which we transport a trapped ultracold cloud of 87Rb over a
distance of 28 cm from our MOT chamber to the science chamber. The scheme allows us to shift the focus position at constant waist, providing uniform trapping conditions over the full transport length.
Furtheron, with the chosen configuration we can dynamically change the waist size at fixed focus position.

Read the paper : New J. Phys. 16 (2014) 093028

Read the preprint: arxiv:1406.2336

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