Emergent Orders of Spinor BECs in a Multimode Ring Resonator – EOSBECMR

Our experimental approach involved injecting light at 1560 nm into the cavity for atom trapping, and at 780 nm for the probing and manipulation of the atomic ensemble. A milestone achievement was the development of an efficient protocol for loading and cooling rubidium atoms in a telecom dipole trap. This innovative technique, leveraging gray molasses cooling and hyperfine dark states, enabled rapid and coherent cooling within a conservative trap. Crucially, it circumvented the inherent atom losses associated with conventional evaporation methods.
- development of a high spatial and temporal resolution imaging system to observe the atomic dynamic in the cavity
- low intensity detection system to measure the atomic emission in the cavity modes
- advanced electronics (microcontrollers, FPGAs, DDSs) to synchronize and control the complex experimental setup

The experimental setup has been realized in all its components, notably the traveling cavity in
ultra-high-vacuum and the injection of light at 1560 nm for the atom trapping and at 780 nm for atom probing, also with different frequencies simultaneously.

We implemented a high efficiency loading and cooling protocol for Rb atoms in the optical trap, using hyperfine dark states and gray molasses cooling. In this way we could obtain a BEC in TEM00 mode the traveling wave cavity, and also two BECs by exploiting instead the TEM01 mode. The same protocol was key to achieve the first all-optical BEC in micro-gravity, obtained on the 0g simulator that works in Bordeaux, and is currently employed on the weak equivalence principle test with atom carried on on the parabolic flights on the Novespace plane.

We recently observed atom-cavity coupling and Collective Atomic Induced Recoil Lasing (CARL) in the traveling wave resonator, using thermal atomic clouds; the repetition of the same experiments with a BEC is planned in the future, to conclude the project’s objectives achieved only partially. We realized a cavity-aided Raman beamsplitter.

More on the technological side, we developed an open source control system for experiments in AMO physics.

On the theoretical sector the following results have been achieved:
- Study of emergent topological spin textures in a 3-component BEC coupled to a ring cavity;
- Study of synthetic magnetic field generation with a Fermi gas in a cavity;
- Study of quantum nature of the crystallization process in a ring cavity;
- Emergence of a quasi-crystalline symmetry at the superradiant phase transition;
- Study of a new type of gravimeter based on a supersolid phase in a ring cavity;
- Study of tests of quantum gravity with BECs

- Novel loading and cooling protocol for rubidium atoms in telecom dipole traps, relying on grey molasses cooling and hyperfine dark states. The protocol is very efficient, adapt to other atoms and molecules, and allows very fast and lossless cooling within a conservative trap.
- First reported Bose-Einstein condensation in microgravity, using a zero-g simulator performing 600 ms of parabolic flight.
- Realization of a control system for AMO physics experiment, integrating digital, analog and RF signals, allowing a synchronization at the 100 ns level, and provided as an open source project via an online repository.
- Proposition of a new type of purely quantum gravimeter based on a supersolid phase in a traveling wave cavity.
- Study of several emergent phenomena in different cavity configurations, with both BEC and Fermi gases, and realization of an extensive review on the subject by the UIBK group.
- Study of tests of quantum gravity with BECs.

We want also to highlight how the two students who worked on the experimental apparatus quickly found scientific positions to continue their career in quantum sensing (the PhD as a postdoc in Nice – France, the postdoc as a lead scientist for the development of key enabling technologies in quantum sensing at GLOphotonics, Limoges – France). Also the students working on the theoretical side of the project have been succesfull in pursuing their research career.

- Phys. Rev. Lett. 122, 113603 (2019). doi: doi.org/10.1103/PhysRevLett.122.113603
- Phys. Rev. Lett. 122, 190801 (2019). doi: doi.org/10.1103/PhysRevLett.122.190801
- Phys. Rev. Lett., 123, 210604 (2019). doi: doi.org/10.1103/PhysRevLett.123.210604
- Phys. Rev. Lett., 123, 240402 (2019). doi:https://doi.org/10.1103/physrevlett.123.240402
- New. J. Phys. 21, 013029 (2019). doi: doi.org/10.1088/1367-2630/aaf9e3
- Phys. Rev. B 100, 224306 (2019). doi: doi.org/10.1103/PhysRevB.100.224306

- Phys. Rev. Lett., 124, 033601 (2020). doi: doi.org/10.1103/PhysRevLett.124.033601
- Phys. Rev. Res. 2, 013212 (2020). doi: doi.org/10.1103/physrevresearch.2.013212
- Class. Quantum Grav. 37, 225017 (2020). doi:https://doi.org/10.1088/1361-6382/aba80e
- Rev. Sci. Instrum. 91, 033203 (2020). doi:https://doi.org/10.1063/1.5129595

- Phys. Rev. Quantum 2, 010325 (2021). doi:https://doi.org/10.1103/PRXQuantum.2.010325
- Phys. Rev. Lett. 127, 013202 (2021). doi: doi.org/10.1103/PhysRevLett.127.013202
- Phys. Rev. A. 103, 023302 (2021). doi: doi.org/10.1103/PhysRevA.103.023302
- Phys. Rev. Research. 3, 013173 (2021). doi: doi.org/10.1103/PhysRevResearch.3.013173
- New J. Phys. 23, 043020 (2021). doi: doi.org/10.1088/1367-2630/abedff
- Opt. Expr. 29, 27760 (2021). doi: doi.org/10.1364/OE.433179
- Adv. In Phys. 70, 1 (2021). doi: doi.org/10.1080/00018732.2021.1969727
- Sci. Rep. 12, 19000 (2022). doi: doi.org/10.1038/s41598-022-23468-3
- Phys. Rev. Lett. 128, 070603 (2022). doi: doi.org/10.1103/PhysRevLett.128.070603
- Phys. Rev. Lett.
arxiv.org/abs/2201.11693
- A. Bertoldi, S. Gaffet, M. Prevedelli, D.A. Smith, Forecasting ocean wave-induced seismic noise, doi: doi.org/10.21203/rs.3.rs-2755019/v1
- C.-H. Feng, P. Robert, P. Bouyer, B. Canuel, J. Li, S. Das, C. C. Kwong, D. Wilkowski, M. Prevedelli, and A. Bertoldi, Compact and high flux strontium atom source, arXiv:2310.00657 [physics.atom-ph]
- AVS Quantum Sci. 5, 019201 (2023). doi: doi.org/10.1116/5.0098119

The project "Emergent Orders of Spinor BECs in a Multimode Ring Resonator" (EOSBECMR) will achieve a major leap in the field of both theoretical and experimental cavity quantum electrodynamics (QED) by

1) realizing for the first time truly emergent phenomena - such as crystallization, glassiness, supersolidity - with a Bose-Einstein condensates (BEC) coupled to a traveling wave resonator. The degenerate and translationally invariant nature of a traveling-wave ring cavity allows one to simulate and explore several so far inaccessible phenomena such as the dynamics of defects, melting, phonon-like excitations, crystal frustration, and supersolidity.
2) actualizing a novel approach to reach the long sought quantum magnetic states by generating cavity-photon mediated spin-spin interactions in a BEC within a cavity.
3) implementing cavity-mediated long-range interactions between independent BECs exploiting the fact that the bow-tie traveling wave cavity can form 1D, 2D and 3D arrays of optical traps, within which multiple independent BECS can be created. The target is to obtain massive entanglement between the two components of a single BEC, and for the first time between two independent BECs. The realization of a network of entangled condensates will represent a breakthrough for quantum communication protocols.
4) studying novel phenomena, such as topological phases and supersolidity, emerging from the competition between cavity-mediated long-range interactions and collisional contact interactions as well as quantum statistics.

The French partner will study these systems experimentally with an existing cavity-BEC setup, where they have already obtained arrays of condensates using the high order modes of the resonator. The French partner plan to characterize the ordered states resulting from the phase transitions implementing G2 spectroscopy in a novel fashion, by combining measurements from both the atoms and the photons transmitted by the cavity. The Austrian partner will theoretically study cavity induced synthetic gauge fields and long-range interactions in both bosonic and fermionic systems, with the aim of characterizing the dynamical gauge fields and identifying its influence on the Dicke superradiance phase transition and emergent orders. The possibility of implementing dynamic gauge potentials in a cavity could open the way to simulate gauge theories like quantum chromodynamics (QCD) and ultimately the Standard Model of elementary particles in atomic physics.

This project is an international collaboration between the experimental Cold Atom Group at LP2N (PI A. Bertoldi, D. Naik, and P. Bouyer) - experts in matter wave interferometry, cavity QED, ultracold gases, quantum measurements - and the theoretical group of cavity QED in Innsbruck (PI F. Mivehvar, H. Ritsch, and S. Ostermann) - pioneers of self-ordering and superradiance in optical resonators, and world leaders in cavity optomechanics and cavity cooling.