Periodic Reporting for period 4 - CRITISUP2 (Criticality and Dual Superfluidity)
Période du rapport: 2021-11-01 au 2022-04-30
The CRITISUP2 project is a quantum simulator of one of the most fundamental problems in quantum physics: how to understand the low temperatures phases of spin ½ fermions with arbitrary and tunable attractive interaction. Some aspects of this problem date back to over 50 years. The excellent control of ultracold quantum gases using laser light and the unique tunability of interactions are invaluable tools to answer some of these pending questions.
One of them is the characterization of the critical regime near the superfluid transition for a spin balanced Fermi gas and a second important question is associated to the existence of a long-sought Fulde-Ferrell-Larkin-Ovchinnikov phase in spin-imbalanced gases where Cooper pairs form at finite momentum, displaying a spatially modulated order parameter.
The CRITISUP2 ERC project has several objectives, (i) the exploration of the phase diagram of spin ½ Fermi gases with tunable interaction and the study of associated critical phenomena, and (ii) the study of static and transport phenomena in Bose-Fermi mixtures of lithium isotopes (iii) develop theoretical tools to adress the physics of strongly correlated fermions in a quantitative manner.
One of them is the characterization of the critical regime near the superfluid transition for a spin balanced Fermi gas and a second important question is associated to the existence of a long-sought Fulde-Ferrell-Larkin-Ovchinnikov phase in spin-imbalanced gases where Cooper pairs form at finite momentum, displaying a spatially modulated order parameter.
The CRITISUP2 ERC project has several objectives, (i) the exploration of the phase diagram of spin ½ Fermi gases with tunable interaction and the study of associated critical phenomena, and (ii) the study of static and transport phenomena in Bose-Fermi mixtures of lithium isotopes (iii) develop theoretical tools to adress the physics of strongly correlated fermions in a quantitative manner.
On the experimental side, the Bose-Fermi machine has undergone a major renovation towards an an-optical cooling machine. The project has implemented for the first time simultaneous D1 sub-Doppler cooling of both lithium isotopes to temperatures below 100 microkelvins. This crucial step leads to a considerable simplification of dual isotope machine avoiding the need for evaporation in a magnetic trap.
In parallel a new quantum gas machine operating with lithium 6 fermions has been constructed and achieved deep quantum degeneracy and fermionic superfluidity. 4x104 lithium atoms are cooled to a temperature as low as 0.08 times the Fermi temperature with a total duration of 15 seconds. This repetition rate is 6 times faster than in our previous quantum gas machine that used lithium 7 bosons to cool the spin ½ lithium 6 fermions and at the state of the art for a dual chamber machine.
Quantum degeneracy has been characterized by a precision measurement of the equation of state at unitarity and comparison with previous measurements at MIT and ENS, and with theory performed within the project (See below) for the spin-balanced gas. We have also observed a plateau on the doubly-integrated density difference of in-situ images when the gas is spin polarized. As shown in the past, this is a hallmark of superfluid pairing at the center of the trapped atom cloud. First results on matter-wave diffraction of a lithium dimer molecular Bose-Einstein condensate have recently been obtained. The machine is very versatile, enabling studies of phase transitions both in bulk or lattice geometries. The science glass cell has large optical access and good optical quality windows for high resolution imaging of individual fermions in tailored optical potentials. This constitutes the next step of CRITISUP2 on this new machine. For this purpose, we have designed and constructed the laser system for confining the individual atoms into a deep three-dimensional optical lattice and performing Raman sideband cooling for about one second to achieve spin-resolved single atom detection through fluorescence imaging.
On the theory side of CRITISUP2, we consider the unitary Fermi gas, the textbook-model of non-relativistic fermions in three-dimensional continuous space that accurately describes our experiments. We have shown that summing up series of Feynman diagrams can yield unbiased accurate results for strongly-correlated fermions even when the convergence radius vanishes. We have produced an accurate equation of state of the normal phase of the low temperature unitary gas and reconciled experimental data measured previously in our group and at MIT with the theoretically conjectured fourth-virial coefficient. This was obtained by summing up to 10^5 irreducible Feynman diagrams, a new feature possible with a diagrammatic Monte Carlo approach. A powerful quantum algorithm called connected determinant Monte Carlo method was introduced by R. Rossi during his PhD in the group. We showed that the diagrammatic series for the unitary Fermi actually diverges as N factorial to the power 1/5 and using an appropriate conformal Borel transformation we were able to give a solid mathematical meaning to our previous calculations with even smaller error bars. We also computed the contact parameter which is found in good agreement with the MIT and Swinburne University experimental results. The contact characterizes numerous properties of the quantum gas such as the momentum distribution at large momenta or the pair correlation function at short distances. We have obtained accurate data for the contact and the momentum distribution of the unitary gas in the normal phase, using bold diagrammatic Monte Carlo and Borel resummation. Our results allow to discriminate between previous theoretical predictions, which differed substantially even at the qualitative level, and provide crucial benchmarks for the development of precision measurements.
A detailed description of the diagrammatic Monte Carlo algorithm for the resonant Fermi gas in the normal Phase with incorporation of ultraviolet asymptotics has also been published. Apart from the self-consistent bold scheme, we also describe a non-self-consistent scheme, for which the ultraviolet treatment is more involved.
On the subject of Bose-Fermi superfluid mixtures, we have studied several theoretical questions raised by our previous experiments. First, we have investigated the properties of an impurity immersed in a superfluid of strongly correlated spin 1/2 fermions. For resonant interactions, we have related the stability diagram of dimer and trimer states to the three-body problem for an impurity interacting with a pair of fermions. We have calculated beyond-mean-field corrections to the energy of the impurity in the weakly interacting regime where these corrections are divergent and have to be regularized by properly accounting for three-body physics.
Second, we have modeled the dynamics of two harmonically trapped counterflowing superfluids. Using complementary analytical and numerical approaches, we studied the shedding of elementary excitations triggered by the relative motion of the two species. We exhibited two different excitation mechanisms leading to distinct threshold velocities for the onset of dissipation: in addition to the parametric pair production present in homogeneous, galilean-invariant systems, we showed that non-uniform motion and density inhomogeneities allow for a Landau-like decay mechanism where single excitations are produced.
In parallel a new quantum gas machine operating with lithium 6 fermions has been constructed and achieved deep quantum degeneracy and fermionic superfluidity. 4x104 lithium atoms are cooled to a temperature as low as 0.08 times the Fermi temperature with a total duration of 15 seconds. This repetition rate is 6 times faster than in our previous quantum gas machine that used lithium 7 bosons to cool the spin ½ lithium 6 fermions and at the state of the art for a dual chamber machine.
Quantum degeneracy has been characterized by a precision measurement of the equation of state at unitarity and comparison with previous measurements at MIT and ENS, and with theory performed within the project (See below) for the spin-balanced gas. We have also observed a plateau on the doubly-integrated density difference of in-situ images when the gas is spin polarized. As shown in the past, this is a hallmark of superfluid pairing at the center of the trapped atom cloud. First results on matter-wave diffraction of a lithium dimer molecular Bose-Einstein condensate have recently been obtained. The machine is very versatile, enabling studies of phase transitions both in bulk or lattice geometries. The science glass cell has large optical access and good optical quality windows for high resolution imaging of individual fermions in tailored optical potentials. This constitutes the next step of CRITISUP2 on this new machine. For this purpose, we have designed and constructed the laser system for confining the individual atoms into a deep three-dimensional optical lattice and performing Raman sideband cooling for about one second to achieve spin-resolved single atom detection through fluorescence imaging.
On the theory side of CRITISUP2, we consider the unitary Fermi gas, the textbook-model of non-relativistic fermions in three-dimensional continuous space that accurately describes our experiments. We have shown that summing up series of Feynman diagrams can yield unbiased accurate results for strongly-correlated fermions even when the convergence radius vanishes. We have produced an accurate equation of state of the normal phase of the low temperature unitary gas and reconciled experimental data measured previously in our group and at MIT with the theoretically conjectured fourth-virial coefficient. This was obtained by summing up to 10^5 irreducible Feynman diagrams, a new feature possible with a diagrammatic Monte Carlo approach. A powerful quantum algorithm called connected determinant Monte Carlo method was introduced by R. Rossi during his PhD in the group. We showed that the diagrammatic series for the unitary Fermi actually diverges as N factorial to the power 1/5 and using an appropriate conformal Borel transformation we were able to give a solid mathematical meaning to our previous calculations with even smaller error bars. We also computed the contact parameter which is found in good agreement with the MIT and Swinburne University experimental results. The contact characterizes numerous properties of the quantum gas such as the momentum distribution at large momenta or the pair correlation function at short distances. We have obtained accurate data for the contact and the momentum distribution of the unitary gas in the normal phase, using bold diagrammatic Monte Carlo and Borel resummation. Our results allow to discriminate between previous theoretical predictions, which differed substantially even at the qualitative level, and provide crucial benchmarks for the development of precision measurements.
A detailed description of the diagrammatic Monte Carlo algorithm for the resonant Fermi gas in the normal Phase with incorporation of ultraviolet asymptotics has also been published. Apart from the self-consistent bold scheme, we also describe a non-self-consistent scheme, for which the ultraviolet treatment is more involved.
On the subject of Bose-Fermi superfluid mixtures, we have studied several theoretical questions raised by our previous experiments. First, we have investigated the properties of an impurity immersed in a superfluid of strongly correlated spin 1/2 fermions. For resonant interactions, we have related the stability diagram of dimer and trimer states to the three-body problem for an impurity interacting with a pair of fermions. We have calculated beyond-mean-field corrections to the energy of the impurity in the weakly interacting regime where these corrections are divergent and have to be regularized by properly accounting for three-body physics.
Second, we have modeled the dynamics of two harmonically trapped counterflowing superfluids. Using complementary analytical and numerical approaches, we studied the shedding of elementary excitations triggered by the relative motion of the two species. We exhibited two different excitation mechanisms leading to distinct threshold velocities for the onset of dissipation: in addition to the parametric pair production present in homogeneous, galilean-invariant systems, we showed that non-uniform motion and density inhomogeneities allow for a Landau-like decay mechanism where single excitations are produced.
See main part above: the fast production of Fermi degenerate spin ½ systems will be particularly important when analyzing fluctuations near criticality. The single atom detectivity with sub-micron optical resolution will be an essential tool for detecting Fulde-Ferell-Larkin-Ovchinikov phases, one of the main goals of CRITISUP2.
The development of bold/determinant diagrammatic Monte-Carlo methods for strongly correlated Fermi gases is highly non-conventional. It is pushing the frontier of numerical methods with exact solutions and of quantum simulation with precision comparisons with experimental results.
The development of bold/determinant diagrammatic Monte-Carlo methods for strongly correlated Fermi gases is highly non-conventional. It is pushing the frontier of numerical methods with exact solutions and of quantum simulation with precision comparisons with experimental results.