We propose a general and non-destructive probing scheme to detect and characterize the superfluid excitation spectrum of cold atoms in optical lattices. The protocol relies on a local collisional interaction between an embedded impurity and the surrounding atomic ensemble. By tuning a few controllable external parameters the impurity-lattice interaction can be engineered and information regarding the dispersion relation of the superfluid phonons can be reliably extracted. We describe the general theory and provide an example to show its validity.
We propose a general and non-destructive probing scheme to detect and characterize the superfluid excitation spectrum of cold atoms in optical lattices. The protocol relies on a local collisional interaction between an embedded impurity and the surrounding atomic ensemble. By tuning a few controllable external parameters the impurity-lattice interaction can be engineered and information regarding the dispersion relation of the superfluid phonons can be reliably extracted. We describe the general theory and provide an example to show its validity.
We present a general and non-invasive probing scheme to perform full momentum-resolved spectroscopy of a cold atomic gas loaded into an optical lattice using a single quantum impurity. The protocol relies on weak collisional interactions and subsequent population measurements of the impurity. By tuning a few controllable external parameters the impurity-lattice interaction can be engineered, and using two sets of measurements, performed with the impurity in two different positions, the full dispersion relation of the superfluid phonons can be reliably extracted.
We study a two-level impurity coupled locally to a quantum gas on an optical lattice.For statedependent interactions between the impurity and the gas, we show that its evolution encodes information on the local excitation spectrum of the gas at the coupling site.Based on this, we design a nondestructive method to probe the system's excitations in a broad range of energies by measuring the state of the probe using standard atom optics methods.We illustrate our findings with numerical simulations for quantum lattice systems, including realistic dephasing noise on the quantum probe, and discuss practical limits on the probe dephasing rate to fully resolve both regular and chaotic spectra.
Quantum probing is a fairly wide topic deepening its roots into many fields as it can borrow tools from, and be applied to, many-body physics, open quantum systems theory, quantum information and quantum thermodynamics. Its wide range of applicability, i.e. the diverse systems under investigations and their specific properties, contributes in making a general theory of quantum probing a rather challenging, if not impossible, task. Despite the need to specialize the probing technique to the various physical systems, we have identified a leitmotiv in our probing approach. Specifically, we will consider a perturbation potential acting as the source of the probing procedure, in most cases this will be an impurity in the complex environment acting as quantum probe. We will generally quantify the information exchange between the probe and its environment, and explore the connection to the concept of non-Markovian, i.e. memoryless, quantum dynamics. This thesis aims at discussing probing protocols for atomic systems confined in optical lattices, both fermionic and bosonic species, as well as trapped ions. The systems inquired can be currently implemented in the field of ultra cold atoms, where they have attracted interest as ideal candidates for quantum simulators and quantum technologies. We will show how to design protocols in which these cold many-body systems act as an environment to a quantum probe, often designed as an impurity atom. Exploiting tools from open quantum systems theory we will discuss how to detect, from the dynamics of the probe, the characteristics of the complex environment. The key idea is to use the quantum probe as read-out device, the properties of the environment are then inferred trough measurements performed exclusively on the probe. Quantities of interest will be related to the environment energy spectrum, equilibrium properties and temperature. The quantum probing paradigm will also allow us to investigate critical phenomena such as phase transitions and orthogonality catastrophe. Finally, we will show how the memory effects induced in the reduced dynamics of an immersed quantum probe can witness, to some extent, the character of the excitations of the environment hinting to a natural link between non-Markovianity and localisation phenomena.
In the past fifteen years ultracold atoms confined to optical lattices, which are artificial crystals of light, have proven to be powerful tools in the study of strongly correlated many-body systems widely known from a condensed matter context. The detailed knowledge, high tunability and control of microscopic parameters has enabled the creation and control of highly non-trivial quantum systems for which a direct comparison of model calculations to experimental measurements is now possible. In order to gain precise information on the properties of ultracold gases in optical lattices, many powerful methods have been developed. In particular spectroscopic methods have enabled to probe different characteristic excitations. However, many fascinating properties of strongly interacting quantum many-body systems are not yet fully characterized. Therefore, this thesis explores further possibilities of lattice modulation spectroscopy which is a time-periodic modulation of the optical lattice amplitude. We theoretically investigate the response of different (mostly one-dimensional) cold atom systems to a lattice modulation by means of the time-dependent density matrix renormalization group method and different analytical approximations. In addition to the normal lattice modulation, we consider a superlattice modulation scheme where the lattice amplitude is modulated in a dimerized fashion, coupling to a certain class of excitations in the system. The lattice modulation spectroscopy is a versatile probe which we use to study different situations relevant for experimental applications. We show that a detection of signatures of the exotic bond order wave phase is feasible in a system of interacting fermions on a one-dimensional optical lattice with staggered energy offset. Moreover, we demonstrate that a temperature measurement of fermions confined to an optical lattice is possible as well as a determination of the interaction strength of bosonic atoms confined to a one-dimensional optical lattice. In addition, various excitations in all these systems are investigated in detail.
We prepare a Bose-Einstein condensed gas in a three-dimensional optical lattice and study the excitation spectrum of the superfluid phase for different interaction strengths. We probe the response of the system by modulating the depth of the optical lattice along one axis. The interactions can be controlled independently by varying the tunnel coupling along the other two lattice axes. In the weakly interacting regime we observe a small susceptibility of the superfluid to excitations, while for stronger interactions an unexpected resonance appears in the excitation spectrum. In addition we measure the coherent fraction of the atomic gas, which determines the depletion of the condensate.
In this paper we show that the superfluidity of cold spin-1 Bose atoms of weak interactions in an optical lattice can be realized according to the excitation energy spectrum which is derived by means of Bogliubov transformation. The characteristic of the superfluid-phase spectrum is explained explicitly in terms of the nonvanishing critical velocity, i.e., the Landau criterion. It is observed that critical velocities of superfluid are different for three spin components and, moreover, can be controlled by adjusting the lattice parameters in practical experiments to detect the superfluid phase.