In the fundamental laws of physics, gauge fields mediate the interaction between charged particles. An example is the quantum theory of electrons interacting with the electromagnetic field, based on U(1) gauge symmetry. Solving such gauge theories is in general a hard problem for classical computational techniques. Although quantum computers suggest a way forward, large-scale digital quantum devices for complex simulations are difficult to build. We propose a scalable analog quantum simulator of a U(1) gauge theory in one spatial dimension. Using interspecies spin-changing collisions in an atomic mixture, we achieve gauge-invariant interactions between matter and gauge fields with spin- and species-independent trapping potentials. We experimentally realize the elementary building block as a key step toward a platform for quantum simulations of continuous gauge theories.

The softness of elastic atomic collisions, defined as the average number of collisions each atom undergoes until its energy decorrelates significantly, can have a considerable effect on the decay dynamics of atomic coherence. In this paper we combine two spectroscopic methods to measure these dynamics and obtain the collisional softness of ultra-cold atoms in an optical trap: Ramsey spectroscopy to measure the energy decorrelation rate and echo spectroscopy to measure the collision rate. We obtain a value of 2.5 (3) for the collisional softness, in good agreement with previously reported numerical molecular dynamics simulations. This fundamental quantity was used to determine the s-wave scattering lengths of different atoms but has not been directly measured. We further show that the decay dynamics of the revival amplitudes in the echo experiment has a transition in its functional decay. The transition time is related to the softness of the collisions and provides yet another way to approximate it. These conclusions are supported by Monte Carlo simulations of the full echo dynamics. The methods presented here can allow measurements of a generalized softness parameter for other two-level quantum systems with discrete spectral fluctuations.Elastic collisions are of great importance in atomic physics, both from a theoretical and a practical point of view. They are relevant for atomic clocks, metrology, quantum information, evaporative cooling, atom-ion hybrid systems and more [1][2][3][4][5][6]. Collisions may also have a significant effect on the coherence properties of an ensemble of atoms, providing either elongation [7][8][9][10][11][12][13][14][15][16] or shortening [17,18] of the atomic coherence time.Considering a rapid collisional process compared to other dynamical timescales [19], there exist two extremities for a colliding atom in the center-of-mass frame of the interacting ensemble: "hard collisions", in which the energy of the atom is completely randomized after a single collision, and "soft collisions" in which the atomic energy remains almost unchanged after each collision [14]. We therefore define the "collisional softness" parameter, s, as the number of times an atom has to collide in order for the correlation between its initial and final energies to drop to 1/e [20]. The collisional softness of hard collisions is one, since the energy correlation drops to zero after a single collision. Collisions are considered "soft" if their softness parameter is much larger than unity. Even though the s-wave collisional process considered here is itself is of universal nature, the softness of the collisions can be affected by the confining potential. This can be intuitively understood by considering that only the kinetic energy changes due to a collision whereas the potential energy does not, carrying a "memory" of the energy prior to the collision.More formally, an ensemble of colliding trapped thermal atoms has two relevant characteristic rates. First, the atomic collisions, treated as a Poisson process ener...

We perform Raman spectroscopy of optically trapped non interacting 87 Rb atoms, and observe revivals of the atomic coherence at integer multiples of the trap period. The effect of coherence control methods such as echo and dynamical decoupling is investigated experimentally, analytically and numerically, along with the effect of the anharmonicity of the trapping potential. The latter is shown to be responsible for incompleteness of the revivals. Coherent Raman control of trapped atoms can be useful in the context of free-oscillation atom intefrerometry and spatial multi-mode quantum memory.Coherent control of cold neutral atomic ensembles can be used for a variety of studies and applications in physics, such as metrology, quantum information, quantum simulators, and fundamental quantum mechanics [1][2][3][4][5][6]. Long coherence times usually imply the need to minimize perturbations on the atoms, as implemented in atomic fountain clocks and atom interferometers. However, in some cases, such as quantum memory [7][8][9][10][11][12][13], there arises also a need for long coherence times in trapped samples. This approach involves challenges such as the inhomogeneous profile of both the external potential and the atomic density [14] and elastic atomic collisions. Coherence has also been shown to revive, in the deep quantum regime, via interaction mechanisms in a Bose-Einstein condensate [15,16].Quantum control of the internal state of a trapped atom can be achieved by the use of microwave (MW) radiation, allowing extremely long coherence times [17][18][19][20][21][22] and enabling the implementation of atom-chip clocks and single-pixel quantum memories.There are, however, applications for which MW control does not suffice. In two-photon stimulated Raman control the momentum recoil is given byhk eff ≈ 2hk sin (α/2), whereh is the reduced Planck constant, k is the wave number of the Raman beams and α is the angle between them. By changing the angle α, the momentum recoilhk eff can be varied between practically zero and 2hk. This allows coupling to the external degrees of freedom of the atoms and the possibility of implementation of spatial multi-mode quantum memory [23,24].Raman atomic coherence in a trap is closely related to the fringe contrast of guided interferometers [25][26][27][28], and more specifically free-oscillation atom interferometers [26,[29][30][31][32][33][34]. These rely on the classical turning points of an underlying harmonic potential for the mirroring of the wave packets. A thermal atom free-oscillation Raman interferometer allows for Ramsey π/2 → π/2 interferometry which is completely impossible to perform in freespace, utilizing the periodicity of the trapping potential. This type of interferometer is sensitive to time-dependent * Current address: Kirchhoff-

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