&Bullet; physics 14, 74

A method that enables far-reaching interactions between fermions on a lattice enables atomic quantum simulations of exotic quantum many-body phenomena.

Currently, one of the best ways to model complex quantum systems is in atomic quantum simulations. The control of the interactions between atoms is the key to such simulations, which can be achieved in atomic lattices with the established “Feshbach resonance” approach. While this approach can be used to vary the strength of short-range interactions between atoms, it does not carry over to long-range interactions, so some interesting quantum systems are outside the scope of the technique. Elmer Guardado-Sanchez of Princeton University and colleagues have now shown that such interactions can be controlled over great distances using the “Rydberg Association” in a lithium grid (

${}^{6th}\text{Li}$

) Atoms [1] . The team’s demonstration opens up unprecedented opportunities for exploring systems that exhibit rich fermionic many-body physics.

In the Feshbach resonance approach to interaction control, a variable magnetic field is used to tune the scattering dynamics of colliding atoms. The use of this technique has led to the experimental observation of the transition between the Bose-Einstein condensation regime (BEC), in which strongly interacting fermions form boson molecules, and the Bardeen-Cooper-Schrieffer regime (BCS), in which it is weakly interacting Fermions form loosely bound Cooper pairs. Quantum phenomena that can be simulated with such interactions range from electron correlations behind high-temperature superconductors to quantum kinematics in distant neutron stars. Despite this versatility, an important class of systems remains beyond the reach of simulations based on local interactions. These systems consist of spinless fermions which, according to the Pauli exclusion principle, are not allowed to sit on top of each other, which means that local interactions are largely irrelevant. Instead, the remote interactions must be controlled.

One possibility to construct such long-range interactions between spinless atomic fermions is to excite the atoms into Rydberg states, in which an electron occupies a high orbital. This method has been proposed theoretically to convey correlated waves with topological density within a fermionic system [2] . Guardado-Sanchez and colleagues are now applying the technique experimentally, which they do with an ensemble of spinless, fermionics

${}^{6th}\text{Li}$

Atoms.

The team cooled a dilute gas from

${}^{6th}\text{Li}$

Atoms in an optical lattice to a “quantum degenerate” temperature at which the de Broglie wavelength of each atom becomes greater than the interatomic distance. Since the atoms cannot reach the ground state at the same time due to the Pauli exclusion principle, they “freeze” one after the other with the lowest available momentum and form a “Fermi sea” (Fig. 1). In this “sea” state, the atoms hardly interact and there are both minimal thermal and minimal quantum fluctuations.

The team’s next step was to use a laser to implement a Rydberg dressing scheme that mixes the internal ground state of the system with a highly excited Rydberg state. An atom in a Rydberg state shows a larger electrical dipole moment than one in the ground state because of the greater distance between its ion nucleus and its outermost electron. This dipole moment enhancement creates an effective “soft-core interaction” between Rydberg-clad atoms, which means that the strength of the interaction remains roughly constant as the distance between the particles increases, before decreasing over a threshold length scale [2–4] . The researchers show that they can influence the strength and range of this interaction by varying the intensity and frequency of the laser. Although the interaction induced by the Rydberg lattice is isotropic across the two-dimensional system, the movement (through quantum tunneling) of the fermions is limited to one dimension. This restricted freedom of movement hinders the infamous “Rydberg avalanche loss” process, in which Rydberg atoms collide, gain kinetic energy and escape the trap.

The remote interaction and the resulting jumping movement of the fermions generate many-body excitations on the Fermi Sea – commonly referred to as quantum fluctuations. These collective quantum fluctuations can have enormously rich features and give rise to many kinds of quantum-correlated states of matter. The types of phenomena that occur in such a system of interacting fermions depend on the way in which the fermions “pair”, or more precisely on the impulses of the fermions involved and the Cooper pairs that result from them . These momentum-dependent interactions are in turn largely determined by the area of ​​interaction relative to the grid spacing. A soft-core interaction with an adjustable length, as implemented by Guardado-Sanchez and colleagues, could lead to numerous impulse-dependent behaviors that, for example, generate topological density waves [2] and chiral

$p+Ip$

Redundancy [5] . Such

$p+Ip$

Superfluids support topological Majorana vortices and offer a plausible way of realizing topological quantum computations.

Even more exotic and counterintuitive phenomena can occur when different pairing possibilities occur at the same time. Although midfield theories typically predict that superfluidity occurs in purely attractive interactions, calculations of the functional renormalization groups suggest that a complex combination of different fermion pairings should yield unconventional results. “f-Wave superfluidity even with atomic repulsion [6] . Guardado-Sanchez and colleagues have so far only shown attractive interactions, but a coordination of attraction to repulsion is possible experimentally [7] . Interesting effects should also occur when the interaction strength completely dominates the kinetic energy and the system is then driven towards a Wigner crystal or a fractional quantum Hall state [8, 9] .

In the team’s experiment with its lattice-hopping fermions, the dynamic aspects of the system can be observed more easily than the quantum many-body equilibrium states. Uncovering how such conditions can be investigated in a non-equilibrium environment should stimulate future theoretical research. On the application side, in addition to the above-mentioned potential for topological quantum computing, the control of interactions over a long range is an important step in carrying out quantum simulations of problems in quantum chemistry. Such simulations represent an arena that is ripe for applications in which the so-called “quantum advantage” is used to solve problems that could not be solved with conventional computers. One of the strengths of the team scheme in realizing applications is that, in contrast to previously developed Feshbach resonance techniques, it is magnetic field-free. This aspect offers additional freedom when integrating the technology into certain cold atom quantum technologies that are sensitive to magnetic fields, such as e.g. B. artificial calibration fields.

## References

1. E. Guardado-Sanchez et al., “Extinguishing dynamics of a Fermi gas with strong non-local interactions” Phys. Rev. X.11021036 (2021).
2. X. Li and S. Das Sarma, “Waves of exotic topological density in cold atomic Rydberg-clad fermions”, Nat. Commun.6th7137 (2015).
3. G. Pupillo et al., “Strongly Correlated Gases from Rydberg-Clad Atoms: Quantum and Classical Dynamics” Phys. Rev. Lett.104223002 (2010).
4. N. Henkel et al., “Three-dimensional roton excitations and super solid formation in Rydberg-excited Bose-Einstein condensates” Phys. Rev. Lett.104195302 (2010).
5. B. Xiong et al., “Topological superfluid due to blockage effects in a Rydberg-clad Fermi gas” Phys. Rev. A.90013631 (2014).
6. A. Keleş et al., “f -Wave superfluidity through repulsive interaction in Rydberg-clad Fermi gas ” Phys. Rev. A.101023624 (2020).
7. M. Saffman et al., “Quantum information with Rydberg atoms”, Rev. Mod. Phys.822313 (2010).
8. T. Grass et al., “Fractional Quantum Hall Phases of Bosons with Adjustable Interactions: From the Laughlin Liquid to a Fractional Wigner Crystal” Phys. Rev. Lett.121253403 (2018).
9. DN Sheng et al., “Fractional quantum Hall effect in the absence of Landau levels” Nat. Commun.2389 (2011).

Xiaopeng Li is Professor of Physics at the Physics Institute of Fudan University in China and is jointly employed by the Shanghai Qi Zhi Institute. He is active in quantum information science and condensed matter theories, with his main research interest being harnessing the quantum computational power of various quantum simulation platforms. He received his Ph.D. He graduated from the University of Pittsburgh with a degree in physics in 2013 and joined Fudan University as a faculty member in 2016 after spending three years at the University of Maryland, supported by a postdoctoral theoretical scholarship from the Joint Quantum Institute. He has been a full professor since 2019.