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Josephsonin ilmiö ultrakylmissä fermikaasuissa

Heikkinen, Miikka

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

This master's thesis studies the theory of ultracold atomic Fermi gases. A system of two BCS superfluids coupled with radio frequency fields is studied as an analogue of the Josephson junction in ultracold gases. This system is shown to display an asymmetric Josephson effect, which is a genuine expansion of the Josephson effect encountered in solid state physics. Finite temperature effects and interactions between the two BCS superfluids are shown to enrich the dynamics of the system further, leading for example to a phase difference between two components of the alternating Josephson current.

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Spin-asymmetrinen Josephsonin ilmiö optisissa superhiloissa

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arXiv:cond-mat/0204376•Physical Review A•Oct 24, 2002•22 citations

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•Jan 1, 2010•1 citation
This master's thesis studies the theory of ultracold atomic Fermi gases. A system of two BCS superfluids coupled with radio frequency fields is studied as an analogue of the Josephson junction in ultracold gases. This system is shown to display an asymmetric Josephson effect, which is a genuine expansion of the Josephson effect encountered in solid state physics. Finite temperature effects and interactions between the two BCS superfluids are shown to enrich the dynamics of the system further, leading for example to a phase difference between two components of the alternating Josephson current.
This master's thesis studies the competition and the coexistence of pairing modes in three-component ultracold Fermi gases. The system is considered to be in a homogeneous potential or in a spherically symmetric harmonic trap. In the homogeneous potential different treatments of chemical potentials lead to qualitatively different pairing schemes. In the harmonic trap, local density approximation gives the thermodynamical limit, but Bogoliubov-de Gennes method takes into account finite size effects. Both methods suggest that the coexistence of several pairing gaps only exists in a symmetric case at the thermodynamical limit. In addition, the population imbalances can lead to qualitatively different, possibly non-BCS pairing schemes. The radio-frequency(RF-) spectroscopy is an experimental method for measuring the pairing gap. The RF-spectra reveal the underlying pairing scheme in the three-component system. The coexistence of two pairing gaps can give rise to novel kind of superfluid current flowing between mutually non-paired components. This anomalous current possesses features similar to the Josephson effect, but the phenomenon is qualitatively different and new.
This work considers the theory of ultracold Fermi gases. We study the spin-asymmetric Josephson effect where the spin components of a Cooper pair feel spin-dependent potentials during the tunneling process and as a result oscillate at the same Josephson frequency but with different amplitudes. This contrasts the conventional interpretation of the Josephson effect in which the Cooper-paired spins 'tunnel together'. Here, we propose a new experimental arrangement to detect the yet-unobserved spin-asymmetric Josephson effect. We investigate two-component fermions in a one-dimensional spin-dependent optical superlattice described by a Fermi-Hubbard Hamiltonian and simulate the dynamics of the set-up with the essentially exact time-evolving block decimation (TEBD) numerical method. We demonstrate that the characteristics of the spin-asymmetric Josephson effect, frequency-synchronized particle number oscillations with spin-asymmetric critical currents, are present in the system. We show that the Josephson frequency depends only on the sum of the spin-dependent potential offsets between two adjacent sites in the super-lattice. We further exhibit that significant asymmetries of over 10% in the critical currents of the spin components are feasible. We also evince that the properties of the particle currents in the super-lattice system agree with the analytical results given by a Hubbard dimer model consisting of only one unit cell of the super-lattice in the strongly interacting limit.
This thesis presents experiments investigating the phase diagram of ultracold atomic Fermi gases using radio-frequency spectroscopy. The tunability of many experimental parameters including the temperature, the interparticle interaction strength and the relative population of different Fermions allows to access very different physical regimes. Radio-frequency spectroscopy has been developed into an ideal tool to probe correlations between particles in these different phases. In particular, radio-frequency spectroscopy of highly population imbalanced atomic Fermi systems gives access to the impurity problem: A single Fermion, or Boson, immersed in a sea of Fermions constitutes a polaron, which can be described by Landau's Fermi liquid theory. A critical interaction strength can be identified separating the regime of a fermionic polaron and a bosonic polaron. Radio-frequency spectroscopy of the polarized superfluid phase allows an accurate measure of the superfluid gap [Delta] and allows to identify the importance of Hartree Mean-field energies. Furthermore, it is shown how these different physical regimes are connected.
This thesis studies radio-frequency spectroscopy of superfluid alkali Fermi gases. Radio-frequency and laser fields provide a coherent and well understood tool for manipulating atomic gases. However, new phenomena are expected and have already been seen experimentally when the alkali atoms become strongly interacting. Here we use a simple perturbative treatment of the atom-rf-field coupling for studying the spectroscopy of a strongly interacting gas. At ultracold temperatures fermionic atoms become paired in analogy to electrons in superconductors. The resulting binding energy, or the pairing gap, can be observed as a shift in the radio-frequency spectrum. With strong interactions, the fermions begin pairing already above the critical superfluid transition temperature. The radio-frequency spectroscopy grants a way to study these fluctuation effects quantitatively. The inhomogeneous trapping potential of the atom cloud also adds its own flavour, resulting in distinct mesoscopic effects in the radio-frequency spectra. Our theoretical models are in very good agreement with the experimental results. First order perturbation theory provides qualitatively correct lineshapes, and our generalised perturbative approach gives quantitatively correct magnitudes for the transfer rates. The inhomogeneity plays an important part also in more exotic systems in which the simple BCS-type pairing of atoms is prevented by polarising the gas. Superfluidity and phase separation in such spin-imbalanced gases has been experimentally observed. We have suggested the use of radio-frequency spectroscopy for observing exotic polarised superfluid states, present at the edges of the atom cloud.
In this Thesis we will theoretically address some issues concerning the Physics of ultracold Fermi gases, all of them with experimental relevance. The field of ultracold gases, and more recently of ultracold Fermi gases, is gathering a lot of experimental and theoretical interest for two main reasons: the great control on the relevant parameters of the problem and the relative simplicity of the minimal theory which is able to correctly describe the system. Building upon this solid background, ultracold gases provided an ideal laboratory for testing more refined theories and also for addressing fundamental issues of quantum mechanics as well as for simulating more complex physical systems such as those encountered in condensed matter. Even if the effective hamiltonian of ultracold gases can be simple, due to the diluteness of the system and the low temperature, which imply low energy physics, the solution of the quantum mechanic equations governing the state of these systems is not always simple. For the static properties usually mean-field solutions exist or perturbative expansions can be produced in some regimes. However Quantum Monte Carlo (QMC) techniques provide more accurate results especially in the strongly interacting regimes. For confined systems it is possible to use QMC only for a few particles, so that, for large number of particles, a fruitful combined use of Density Functional Theory (DFT) and QMC is necessary. The study of the dynamics of ultracold gases has received little attention with QMC techniques, due to the intrinsic computational difficulty of the many-body problem, so that general hydrodynamic equations are often used for studying the propagation of smoothly varying perturbations. In this Thesis we use QMC techniques for studying the problem of ferromagnetism in repulsive or effectively repulsive ultracold gases without a lattice and the problem of the Bardeen-Cooper-Schrieffer to Bose-Einstein-Condensation (BCS-BEC) crossover in two dimensions. We use DFT in the Local Density Approximation (LDA) for calculating the density profiles of ultracold Fermi gases in harmonic magneto-optical traps, starting from QMC equations of state. We study the propagation of first and second sound in ultracold Fermi gases in cylindrical geometry, using the hydrodynamic equations of superfluids.