Measuring the one-particle excitations of ultracold fermionic atoms by stimulated Raman spectroscopy

Time-resolved vibrational dynamics: Novel opportunities for sensing and imaging

The evolution of time-resolved spectroscopies has resulted in significant advancements across numerous scientific disciplines, particularly those concerned with molecular electronic states. However, the intricacy of molecular vibrational spectroscopies, which provide comprehensive molecular-level information within complex structures, has presented considerable challenges due to the ultrashort dephasing time. Over recent decades, an increasing focus has been placed on exploring the temporal progression of bond vibrations, thereby facilitating an improved understanding of energy redistribution within and between molecules. This review article focuses on an array of time-resolved detection methodologies, each distinguished by unique technological attributes that offer exclusive capabilities for investigating the physical phenomena propelled by molecular vibrational dynamics. In summary, time-resolved vibrational spectroscopy emerges as a potent instrument for deciphering the dynamic behavior of molecules. Its potential for driving future progress across fields as diverse as biology and materials science is substantial, marking a promising future for this innovative tool.

Probing quantum many-body correlations by universal ramping dynamics

Ramping a physical parameter is one of the most common experimental protocols in studying a quantum system, and ramping dynamics has been widely used in preparing a quantum state and probing physical properties. Here, we present a novel method of probing quantum many-body correlation by ramping dynamics. We ramp a Hamiltonian parameter to the same target value from different initial values and with different velocities, and we show that the first-order correction on the finite ramping velocity is universal and path-independent, revealing a novel quantum many-body correlation function of the equilibrium phases at the target values. We term this method as the non-adiabatic linear response since this is the leading order correction beyond the adiabatic limit. We demonstrate this method experimentally by studying the Bose-Hubbard model with ultracold atoms in three-dimensional optical lattices. Unlike the conventional linear response that reveals whether the quasi-particle dispersion of a quantum phase is gapped or gapless, this probe is more sensitive to whether the quasi-particle lifetime is long enough such that the quantum phase possesses a well-defined quasi-particle description. In the Bose-Hubbard model, this non-adiabatic linear response is significant in the quantum critical regime where well-defined quasi-particles are absent. And in contrast, this response is vanishingly small in both superfluid and Mott insulators which possess well-defined quasi-particles. Because our proposal uses the most common experimental protocol, we envision that our method can find broad applications in probing various quantum systems.

Spectral Function of a Boson Ladder in an Artificial Gauge Field

We calculate the spectral function of a boson ladder in an artificial magnetic field by means of analytic approaches based on bosonization and Bogoliubov theory. We discuss the evolution of the spectral function at increasing effective magnetic flux, from the Meissner to the Vortex phase, focussing on the effects of incommensurations in momentum space. At low flux, in the Meissner phase, the spectral function displays both a gapless branch and a gapped one, while at higher flux, in the Vortex phase, the spectral function displays two gapless branches and the spectral weight is shifted at a wavevector associated to the underlying vortex spatial structure, which can indicate a supersolid-like behavior. While the Bogoliubov theory, valid at weak interactions, predicts sharp delta-like features in the spectral function, at stronger interactions we find power-law broadening of the spectral functions due to quantum fluctuations as well as additional spectral weight at higher momenta due to backscattering and incommensuration effects. These features could be accessed in ultracold atom experiments using radio-frequency spectroscopy techniques.

Measurement of Spectral Functions of Ultracold Atoms in Disordered Potentials

We report on the measurement of the spectral functions of noninteracting ultracold atoms in a three-dimensional disordered potential resulting from an optical speckle field. Varying the disorder strength by 2 orders of magnitude, we observe the crossover from the "quantum" perturbative regime of low disorder to the "classical" regime at higher disorder strength, and find an excellent agreement with numerical simulations. The method relies on the use of state-dependent disorder and the controlled transfer of atoms to create well-defined energy states. This opens new avenues for experimental investigations of three-dimensional Anderson localization.

Antiferromagnetic Correlations in Two-Dimensional Fermionic Mott-Insulating and Metallic Phases

We experimentally study the emergence of antiferromagnetic correlations between ultracold fermionic atoms in a two-dimensional optical lattice with decreasing temperature. We determine the uniform magnetic susceptibility of the two-dimensional Hubbard model from simultaneous measurements of the in situ density distribution of both spin components. At half filling and strong interactions our data approach the Heisenberg model of localized spins with antiferromagnetic correlations. Moreover, we observe a fast decay of magnetic correlations when doping the system away from half filling.

Lattice-Assisted Spectroscopy: A Generalized Scanning Tunneling Microscope for Ultracold Atoms

We propose a scheme to measure the frequency-resolved local particle and hole spectra of any optical lattice-confined system of correlated ultracold atoms that offers single-site addressing and imaging, which is now an experimental reality. Combining perturbation theory and time-dependent density matrix renormalization group simulations, we quantitatively test and validate this approach of lattice-assisted spectroscopy on several one-dimensional example systems, such as the superfluid and Mott insulator, with and without a parabolic trap, and finally on edge states of the bosonic Su-Schrieffer-Heeger model. We highlight extensions of our basic scheme to obtain an even wider variety of interesting and important frequency resolved spectra.

Realizing a Kondo-correlated state with ultracold atoms

We propose a novel realization of Kondo physics with ultracold atomic gases. It is based on a Fermi sea of two different hyperfine states of one atom species forming bound states with a different species, which is spatially confined in a trapping potential. We show that different situations displaying Kondo physics can be realized when Feshbach resonances between the species are tuned by a magnetic field and the trapping frequency is varied. We illustrate that a mixture of 40K and 23Na atoms can be used to generate a Kondo-correlated state and that momentum resolved radio frequency spectroscopy can provide unambiguous signatures of the formation of Kondo resonances at the Fermi energy. We discuss how tools of atomic physics can be used to investigate open questions for Kondo physics, such as the extension of the Kondo screening cloud.

Two-dimensional Fermi liquid with attractive interactions

We realize and study an attractively interacting two-dimensional Fermi liquid. Using momentum-resolved photoemission spectroscopy, we measure the self-energy, determine the contact parameter of the short-range interaction potential, and find their dependence on the interaction strength. We successfully compare the measurements to a theoretical analysis, properly taking into account the finite temperature, harmonic trap, and the averaging over several two-dimensional gases with different peak densities.

Quasiparticle dynamics in a bose insulator probed by interband bragg spectroscopy

We investigate experimentally and theoretically the dynamical properties of a Mott insulator in decoupled one-dimensional chains. Using a theoretical analysis of the Bragg excitation scheme, we show that the spectrum of interband transitions holds information on the single-particle Green's function of the insulator. In particular, the existence of particle-hole coherence due to quantum fluctuations in the Mott state is clearly seen in the Bragg spectra and quantified. Finally, we propose a scheme to directly measure the full, momentum-resolved spectral function as obtained in the angle-resolved photoemission spectroscopy of solids.

Theory of a Fermi-liquid to non-Fermi-liquid quantum phase transition in dimensions d>1

We develop a theory for a generic instability of a Fermi liquid in dimension d>1 against the formation of a Luttinger-liquid-like state. The density of states at the Fermi level is the order parameter for the ensuing quantum phase transition, which is driven by the effective interaction strength. A scaling theory in conjunction with an effective field theory for clean electrons is used to obtain the critical behavior of observables. In the Fermi-liquid phase the order-parameter susceptibility, which is measurable by tunneling, is predicted to diverge for 1<d<3.

Probing non-abelian statistics of Majorana fermions in ultracold atomic superfluid

We propose an experiment to directly probe the non-abelian statistics of Majorana fermions by braiding them in an s-wave superfluid of ultracold atoms. We show that different orders of braiding operations give orthogonal output states that can be distinguished through Raman spectroscopy. Realization of Majorana states in an s-wave superfluid requires strong spin-orbital coupling and a controllable Zeeman field in the perpendicular direction. We present a simple laser configuration to generate the artificial spin-orbital coupling and the required Zeeman field in the dark-state subspace.

Wilson fermions and axion electrodynamics in optical lattices

We show that ultracold Fermi gases in optical superlattices can be used as quantum simulators of relativistic lattice fermions in 3+1 dimensions. By exploiting laser-assisted tunneling, we find an analogue of the so-called naive Dirac fermions, and thus provide a realization of the fermion doubling problem. Moreover, we show how to implement Wilson fermions, and discuss how their mass can be inverted by tuning the laser intensities. In this regime, our atomic gas corresponds to a phase of matter where Maxwell electrodynamics is replaced by axion electrodynamics: a 3D topological insulator.

Simulating the Wess-Zumino supersymmetry model in optical lattices

We study a cold atom-molecule mixture in two-dimensional optical lattices. We show that, by fine-tuning the atomic and molecular interactions, the Wess-Zumino supersymmetry (SUSY) model in 2+1 dimensions emerges in the low-energy limit and can be simulated in such mixtures. At zero temperature, SUSY is not spontaneously broken, which implies identical relativistic dispersions of the atom and its superpartner, a bosonic diatom molecule. This defining signature of SUSY can be probed by single-particle spectroscopies. Thermal breaking of SUSY at a finite temperature is accompanied by a thermal Goldstone fermion, i.e., phonino excitation. This and other signatures of broken SUSY can also be probed experimentally.

Non-Fermi-liquid fixed point for an imbalanced gas of fermions in 1+ϵ dimensions

We consider a gas of two species of fermions with population imbalance. Using the renormalization group in d=1+ϵ spatial dimensions, we show that for spinless fermions and 2>ϵ>0 a fixed point appears at finite attractive coupling where the quasiparticle residue vanishes, and identify this with the transition to Larkin-Ovchinnikov-Fulde-Ferrell order (inhomogeneous superconductivity). When the two species of fermions also carry spin degrees of freedom we find a fixed point indicating a transition to spin density wave order.

Momentum resolved radio frequency spectroscopy in trapped fermi gases

We address recent momentum-resolved radio frequency (rf) spectroscopy experiments, showing how they yield more stringent tests than other comparisons with theory, associated with the ultracold Fermi gases. We demonstrate that, by providing a clear dispersion signature of pairing, they remove the ambiguity plaguing the interpretation of previous rf experiments. Our calculated spectral intensities are in semiquantitative agreement with the data. Even in the presence of a trap, the spectra are predicted to exhibit two BCS-like branches.

Steady-state nonequilibrium density of States of driven strongly correlated lattice models in infinite dimensions

An exact formalism for calculating the retarded and advanced Green's functions of strongly correlated lattice models in a uniform electric field is derived within dynamical mean-field theory. To illustrate the method, we solve for the nonequilibrium density of states of the Hubbard model in both the metallic and Mott-insulating phases at half-filling (with an arbitrary strength electric field) by employing the approximate numerical renormalization group as the impurity solver. This general approach can be applied to any strongly correlated lattice model in the limit of large dimensions.

Exact exponents of edge singularities in dynamic correlation functions of 1D bose gas

The spectral function and dynamic structure factor of bosons interacting by contact repulsion and confined to one dimension exhibit power-law singularities along the dispersion curves of the collective modes. We find the corresponding exponents exactly, by relating them to the known Bethe ansatz solution of the Lieb-Liniger model. Remarkably, the Luttinger liquid theory predictions for the exponents fail even at low energies, once the immediate vicinities of the edges are considered.

Supersymmetry and the Goldstino-like mode in bose-fermi mixtures

Supersymmetry is assumed to be a basic symmetry of the world in many high-energy theories, but none of the superpartners of any known elementary particle have been observed yet. We argue that supersymmetry can also be realized and studied in ultracold atomic systems with a mixture of bosons and fermions, with properly tuned interactions and single particle dispersion. We further show that in such nonrelativistic systems supersymmetry is either spontaneously broken or explicitly broken by a chemical potential difference between the bosons and fermions. In both cases the system supports a sharp fermionic collective mode similar to the Goldstino mode in high-energy physics, due to supersymmetry. We also discuss possible ways to detect this mode experimentally.