Gauge-Theoretic Origin of Rydberg Quantum Spin Liquids.

Recent atomic physics experiments and numerical works have reported complementary signatures of the emergence of a topological quantum spin liquid in models with blockade interactions. However, the specific mechanism stabilizing such a phase remains unclear. Here, we introduce an exact relation between an Ising-Higgs lattice gauge theory on the kagome lattice and blockaded models on Ruby lattices. This relation elucidates the origin of previously observed topological spin liquids by directly linking the latter to a deconfined phase of a solvable gauge theory. By means of exact diagonalization and unbiased quantum Monte Carlo simulations, we show that the deconfined phases extend in a broad region of the parameter space; these states are characterized by a large ground state overlap with resonating valence bond wave functions. These blockaded models include both creation or annihilation and hopping dynamics, and can be experimentally realized with Rydberg-dressed atoms, offering novel and controllable platforms for the engineering and characterization of spin liquid states.

Entanglement-Guided Search for Parent Hamiltonians.

We introduce a method for the search of parent Hamiltonians of input wave functions based on the structure of their reduced density matrix. The two key elements of our recipe are an ansatz on the relation between the reduced density matrix and parent Hamiltonian that is exact at the field theory level, and a minimization procedure on the space of relative entropies, which is particularly convenient due to its convexity. As examples, we show how our method correctly reconstructs the parent Hamiltonian correspondent to several nontrivial ground state wave functions, including conformal and symmetry-protected-topological phases, and quantum critical points of two-dimensional antiferromagnets described by strongly coupled field theories. Our results show the entanglement structure of ground state wave functions considerably simplifies the search for parent Hamiltonians.

Boundary Time Crystals.

In this work we introduce boundary time crystals. Here continuous time-translation symmetry breaking occurs only in a macroscopic fraction of a many-body quantum system. After introducing their definition and properties, we analyze in detail a solvable model where an accurate scaling analysis can be performed. The existence of the boundary time crystals is intimately connected to the emergence of a time-periodic steady state in the thermodynamic limit of a many-body open quantum system. We also discuss connections to quantum synchronization.

Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models.

We present a scheme for measuring Rényi entropies in generic atomic Hubbard and spin models using single copies of a quantum state and for partitions in arbitrary spatial dimensions. Our approach is based on the generation of random unitaries from random quenches, implemented using engineered time-dependent disorder potentials, and standard projective measurements, as realized by quantum gas microscopes. By analyzing the properties of the generated unitaries and the role of statistical errors, with respect to the size of the partition, we show that the protocol can be realized in existing quantum simulators and used to measure, for instance, area law scaling of entanglement in two-dimensional spin models or the entanglement growth in many-body localized systems.

Majorana Quasiparticles Protected by Z_{2} Angular Momentum Conservation.

We show how angular momentum conservation can stabilize a symmetry-protected quasitopological phase of matter supporting Majorana quasiparticles as edge modes in one-dimensional cold atom gases. We investigate a number-conserving four-species Hubbard model in the presence of spin-orbit coupling. The latter reduces the global spin symmetry to an angular momentum parity symmetry, which provides an extremely robust protection mechanism that does not rely on any coupling to additional reservoirs. The emergence of Majorana edge modes is elucidated using field theory techniques, and corroborated by density-matrix-renormalization-group simulations. Our results pave the way toward the observation of Majorana edge modes with alkaline-earth-like fermions in optical lattices, where all basic ingredients for our recipe-spin-orbit coupling and strong interorbital interactions-have been experimentally realized over the last two years.

Non-equilibrium 8π Josephson effect in atomic Kitaev wires.

The identification of fractionalized excitations, such as Majorana quasi-particles, would be a striking signal of the realization of exotic quantum states of matter. While the paramount demonstration of such excitations would be a probe of their non-Abelian statistics via controlled braiding operations, alternative proposals exist that may be easier to access experimentally. Here we identify a signature of Majorana quasi-particles, qualitatively different from the behaviour of a conventional superconductor, which can be detected in cold atom systems using alkaline-earth-like atoms. The system studied is a Kitaev wire interrupted by an extra site, which gives rise to super-exchange coupling between two Majorana-bound states. We show that this system hosts a tunable, non-equilibrium Josephson effect with a characteristic 8π periodicity of the Josephson current. The visibility of the 8π periodicity of the Josephson current is then studied including the effects of dephasing and particle losses.

Observation of chiral edge states with neutral fermions in synthetic Hall ribbons.

Chiral edge states are a hallmark of quantum Hall physics. In electronic systems, they appear as a macroscopic consequence of the cyclotron orbits induced by a magnetic field, which are naturally truncated at the physical boundary of the sample. Here we report on the experimental realization of chiral edge states in a ribbon geometry with an ultracold gas of neutral fermions subjected to an artificial gauge field. By imaging individual sites along a synthetic dimension, encoded in the nuclear spin of the atoms, we detect the existence of the edge states and observe the edge-cyclotron orbits induced during quench dynamics. The realization of fermionic chiral edge states opens the door for edge state interferometry and the study of non-Abelian anyons in atomic systems.

Constrained dynamics via the Zeno effect in quantum simulation: implementing non-Abelian lattice gauge theories with cold atoms.

We show how engineered classical noise can be used to generate constrained Hamiltonian dynamics in atomic quantum simulators of many-body systems, taking advantage of the continuous Zeno effect. After discussing the general theoretical framework, we focus on applications in the context of lattice gauge theories, where imposing exotic, quasilocal constraints is usually challenging. We demonstrate the effectiveness of the scheme for both Abelian and non-Abelian gauge theories, and discuss how engineering dissipative constraints substitutes complicated, nonlocal interaction patterns by global coupling to laser fields.

Atomic quantum simulation of U(N) and SU(N) non-Abelian lattice gauge theories.

Using ultracold alkaline-earth atoms in optical lattices, we construct a quantum simulator for U(N) and SU(N) lattice gauge theories with fermionic matter based on quantum link models. These systems share qualitative features with QCD, including chiral symmetry breaking and restoration at nonzero temperature or baryon density. Unlike classical simulations, a quantum simulator does not suffer from sign problems and can address the corresponding chiral dynamics in real time.

Atomic quantum simulation of dynamical gauge fields coupled to fermionic matter: from string breaking to evolution after a quench.

Using a Fermi-Bose mixture of ultracold atoms in an optical lattice, we construct a quantum simulator for a U(1) gauge theory coupled to fermionic matter. The construction is based on quantum links which realize continuous gauge symmetry with discrete quantum variables. At low energies, quantum link models with staggered fermions emerge from a Hubbard-type model which can be quantum simulated. This allows us to investigate string breaking as well as the real-time evolution after a quench in gauge theories, which are inaccessible to classical simulation methods.

Trimer liquids and crystals of polar molecules in coupled wires.

We investigate pairing and crystalline instabilities of bosonic and fermionic polar molecules confined to a ladder geometry. Combining analytical and numerical techniques, we show that gases of composite molecular dimers as well as trimers can be stabilized as a function of the density difference between the wires. A shallow optical lattice can pin both liquids, realizing crystals of composite bosons and fermions. We show that these exotic quantum phases are robust against conditions of confinement of the molecular gas to harmonic finite-size potentials.

One-dimensional quantum liquids with power-law interactions: the Luttinger staircase.

We study one-dimensional fermionic and bosonic gases with repulsive power-law interactions 1/|x|(ß), with ß>1, in the framework of Tomonaga-Luttinger liquid (TLL) theory. We obtain an accurate analytical expression linking the TLL parameter to the microscopic Hamiltonian, for arbitrary ß and strength of the interactions. In the presence of a small periodic potential, power-law interactions make the TLL unstable towards the formation of a cascade of lattice solids with fractional filling, a "Luttinger staircase." Several of these quantum phases and phase transitions are realized with ground state polar molecules and weakly bound magnetic Feshbach molecules.

Atomic color superfluid via three-body loss.

Large three-body loss rates in a three-component Fermi gas confined in an optical lattice can dynamically prevent atoms from tunneling so as to occupy a lattice site with three atoms. This effective constraint not only suppresses the occurrence of actual loss events, but stabilizes BCS-pairing phases by suppressing the formation of trions. We study the effect of the constraint on the many-body physics using bosonization and density matrix renormalization group techniques, and also investigate the full dissipative dynamics including loss for the example of 6Li.