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Register a new userFluctuations and stochastic processes in one-dimensional many-body quantum systems
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We study the fluctuation properties of a one-dimensional many-body quantum system composed of interacting bosons, and investigate the regimes where quantum noise or, respectively, thermal excitations are dominant. For the latter we develop a semiclassical description of the fluctuation properties based on the Ornstein-Uhlenbeck stochastic process. As an illustration, we analyze the phase correlation functions and the full statistical distributions of the interference between two one-dimensional systems, either independent or tunnel-coupled and compare with the Luttinger-liquid theory.
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The single-particle density is the most basic quantity that can be calculated from a given many-body wave function. It provides the probability to find a particle at a given position when the average over many realizations of an experiment is taken. However, the outcome of single experimental shots of ultracold atom experiments is determined by the $N$-particle probability density. This difference can lead to surprising results. For example, independent Bose-Einstein condensates (BECs) with definite particle numbers form interference fringes even though no fringes would be expected based on the single-particle density [1-4]. By drawing random deviates from the $N$-particle probability density single experimental shots can be simulated from first principles [1, 3, 5]. However, obtaining expressions for the $N$-particle probability density of realistic time-dependent many-body systems has so far been elusive. Here, we show how single experimental shots of general ultracold bosonic systems can be simulated based on numerical solutions of the many-body Schrodinger equation. We show how full counting distributions of observables involving any number of particles can be obtained and how correlation functions of any order can be evaluated. As examples we show the appearance of interference fringes in interacting independent BECs, fluctuations in the collisions of strongly attractive BECs, the appearance of randomly fluctuating vortices in rotating systems and the center of mass fluctuations of attractive BECs in a harmonic trap. The method described is broadly applicable to bosonic many-body systems whose phenomenology is driven by information beyond what is typically available in low-order correlation functions.
Entanglement of spatial bipartitions, used to explore lattice models in condensed matter physics, may be insufficient to fully describe itinerant quantum many-body systems in the continuum. We introduce a procedure to measure the Renyi entanglement entropies on a particle bipartition, with general applicability to continuum Hamiltonians via path integral Monte Carlo methods. Via direct simulations of interacting bosons in one spatial dimension, we confirm a logarithmic scaling of the single-particle entanglement entropy with the number of particles in the system. The coefficient of this logarithmic scaling increases with interaction strength, saturating to unity in the strongly interacting limit. Additionally, we show that the single-particle entanglement entropy is bounded by the condensate fraction, suggesting a practical route towards its measurement in future experiments.
The diagonal elements of the time correlation matrix are used to probe closed quantum systems that are measured at random times. This enables us to extract two distinct parts of the quantum evolution, a recurrent part and an exponentially decaying part. This separation is strongly affected when spectral degeneracies occur, for instance, in the presence of spontaneous symmetry breaking. Moreover, the slowest decay rate is determined by the smallest energy level spacing, and this decay rate diverges at the spectral degeneracies. Probing the quantum evolution with the diagonal elements of the time correlation matrix is discussed as a general concept and tested in the case of a bosonic Josephson junction. It reveals for the latter characteristic properties at the transition to Hilbert-space localization.
In this thesis, I go through the well-known solutions to the one and two-particle systems trapped in a quantum harmonic oscillator and then continue to the three, four and many-body quantum systems. This is done by developing new analytical models and numerical methods both for the few- and many-body systems. One-dimensional systems are very interesting in a sense that particles aligned on a line can only change seats by going through each other. This property can be exploited in the strongly interacting regime, where particles are forced to sit in a specific configuration, which can be easily manipulated. The knowledge of how and where the particles are can be exploited in future quantum applications. In short, the thesis is about establishing a solid knowledge about everything that one needs to know about the one-dimensional few- and many-component interacting quantum systems trapped in harmonic oscillator potentials.
The decoupling of spin and density dynamics is a remarkable feature of quantum one-dimensional many-body systems. In a few-body regime, however, little is known about this phenomenon. To address this problem, we study the time evolution of a small system of strongly interacting fermions after a sudden change in the trapping geometry. We show that, even at the few-body level, the excitation spectrum of this system presents separate signatures of spin and density dynamics. Moreover, we describe the effect of considering additional internal states with SU(N) symmetry, which ultimately leads to the vanishing of spin excitations in a completely balanced system.
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