Related papers: Geometry-induced memory effects in isolated quantu…
We explore the effects of continuous number density measurement on atoms in an optical lattice. By integrating a master equation for quantum observables, we calculate how single particle correlations decay. We consider weakly- and strongly-…
Why do we forget? Why do we remember things that never happened? The conventional answer points to biological hardware. We propose a different one: geometry. Here we show that high-dimensional embedding spaces, subjected to noise,…
In this thesis, I investigate various aspects of one of the most fundamental questions in thermodynamics: what state transformations can quantum systems undergo while interacting with a thermal bath under specific constraints? These…
Electronic properties of quantum materials solids are often well understood via the low energy dispersion of Bloch bands, motivating single band approximations in many metals and semiconductors. However, a closer look reveals length and…
Confining ultracold gases in cavities creates a paradigm of quantum trapping potentials. We show that this allows to bridge models with global collective and short-range interactions as novel quantum phases possess properties of both. Some…
Quantum Hall effects provide intuitive ways of revealing the topology in crystals, i.e., each quantized "step" represents a distinct topological state. Here, we seek a counterpart for "visualizing" quantum geometry, which is a broader…
Cold atoms tailored by an optical lattice have become a fascinating arena for simulating quantum physics. In this area, one important and challenging problem is creating effective spin-orbit coupling (SOC), especially for fashioning a cold…
The digital quantum simulation of lattice gauge theories is expected to become a major application of quantum computers. Measurement-based quantum computation is a widely studied competitor of the standard circuit-based approach. We…
We introduce history-dependent discrete-time quantum random walk models by adding uncorrelated memory terms and also by modifying Hamiltonian of the walker to include couplings with memory-keeping agents. We next numerically study the…
In this work, we have demonstrated that optically generated fictitious magnetic fields can be utilized to extend the lifetime of quantum memories in cold atomic ensembles. All the degrees of freedom of an AC Stark shift such as…
In the measurement of a continuous observable Q, the pure components of the reduced state do, in general, depend on the initial state. For measurements which attempt to localize the measured system in a certain region R, the localized wave…
We introduce an idea of producing an optical lattice relied on the Talbot effect. Our alternative scheme is based on the interference of light behind a diffraction grating in the near-field regime. We demonstrate 1-D and 2-D optical…
The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible…
Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…
Quantum computing has been attracting tremendous efforts in recent years. One prominent application is to perform quantum simulations of electron correlations in large molecules and solid-state materials, where orbital degrees of freedom…
Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be…
A new protocol of the optical quantum memory based on the resonant interactions of the multi atomic system with a cavity light mode is proposed. The quantum memory is realized using a controllable inversion of the inhomogeneous broadening…
A nonrelativistic quantum mechanical particle moving freely on a curved surface feels the effect of the nontrivial geometry of the surface through the kinetic part of the Hamiltonian, which is proportional to the Laplace-Beltrami operator,…
Geometric phase of an open quantum system that is interacting with a thermal environment (bath) is studied through some simple examples. The system is considered to be a simple spin-half particle which is weakly coupled to the bath. It is…
We propose a scheme involving cold atoms trapped in optical lattices to observe different phenomena traditionally linked to quantum-optical systems. The basic idea consists of connecting the trapped atomic state to a non-trapped state…