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Physical review. B, Condensed matter

Reduced quantum fluctuations in the Josephson junction

K. Wódkiewicz

Published Oct 1, 1985• 49 citations
Publisher

Abstract

We predict that a Josephson junction can exhibit, under certain conditions, squeezed or reduced quantum fluctuations of the tunneling current. Using the formal analogy of the Josephson junction to a system of two-level atoms, we show that these reduced fluctuations are closely related to the Bloch-state description of the Bardeen-Cooper-Schrieffer wave function and to the angular-momentum algebra of the proper dynamical variables describing the tunneling process.

DOI
10.1103/physrevb.32.4750

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We predict that a Josephson junction can exhibit, under certain conditions, squeezed or reduced quantum fluctuations of the tunneling current. Using the formal analogy of the Josephson junction to a system of two-level atoms, we show that these reduced fluctuations are closely related to the Bloch-state description of the Bardeen-Cooper-Schrieffer wave function and to the angular-momentum algebra of the proper dynamical variables describing the tunneling process.
A proposal for the generation of a Schr\"odinger-cat-type state is made in the context Josephson junctions. The Bloch state description of the BCS state is used along with the pseudospin algebra description of the tunneling process. The cat state consists of a superposition of Bloch states associated with dc Josephson currents flowing in opposite directions across the junction. The states can be detected by the observation of interference fringes in the probability distribution of the eigenvalues of the Josephson current operator.
Quantum fluctuations of the charge at a current-biased Josephson junction and of the Josephson current couple to the quasiparticle tunneling when the system is at equilibrium in the zero-voltage state. The effect of reducing the capacitance of the junction is studied by means of a model Hamiltonian. When this becomes smaller, charge fluctuations are reduced, but the effective dissipation is also lowered so that the junction displays an underdamped behavior. The Josephson branch is shifted at the voltage e/2C because of charging due to the quasiparticles. A path-integral formulation of the model leads to a high dynamical subgap resistance at I\ensuremath{\rightarrow}0, as recently found experimentally.
Quantum fluctuations are an important feature of isolated systems at low temperatures. This quantum noise is unavoidable due to Heisenberg's uncertainty principle. However, squeezed states can lower the quantum noise in one of a pair of variables at the expense of increasing it in the other variable. This ability to reduce quantum fluctuations makes squeezed states very promising in high-precision measurements. This thesis studies the quantum fluctuation properties of two condensed matter systems: phonons and Josephson junctions. In particular, we theoretically investigate several approaches for the generation and detection of squeezed states in these systems. We study for the first time coherent and squeezed quantum states of phonons, in analogy to the coherent and squeezed states of photons. We introduce and study a lattice amplitude operator, which is the phonon analog of the electric field. Our work provides a clear link between quantum mechanical phonon coherent states and the experimentally observed coherent phonons--typically described in classical terms. We then study phonon squeezed states, which can modulate the quantum fluctuations of atomic displacements below the zero-point quantum noise level. We explore the possibility of generating squeezed phonon states with a variety of different approaches, such as a phonon parametric down-conversion process and a polariton-based mechanism. Furthermore, we propose a possible detection scheme based on reflectivity measurements. We also study quantum fluctuation properties of superconducting Josephson junctions, which have the nonlinear interactions necessary for modulating quantum noise. We obtain approximate ground and excited states, and calculate the variances of the charge and phase in various circuit configurations. This thesis provides a first systematic study of quantum noise and its suppression in condensed matter systems. It also proposes different directions for future studies in the control of quantum noise in solids.
We investigate the superfluid dynamics of a Josephson junction beyond the mean-field description, incorporating the role of thermal fluctuations as well as quantum fluctuations. Using a formalism that accounts for the fluctuations in a homogeneous gas, and under the assumption that the transport of the non-condensed component is negligible, we derive a corrected equation of motion within the two-site approximation. The resulting corrections for the typical dynamical quantities, like the Josephson frequency, the strength of macroscopic quantum self-trapping, and the threshold for spontaneous symmetry breaking, allow us to predict the effects of both types of fluctuations and assess their relative importance in different regimes in a semianalytical fashion. For all the dynamical quantities, the quantum fluctuations are shown to play an opposite role with respect to the thermal fluctuations. Josephson frequency is decreased by thermal fluctuations and both the critical strenghts of macroscopic quantum self trapping and spontaneous symmetry breaking are increased. We assess the experimentally accessible regimes by calculating the relevant parameters of recent experimental realizations of Bosonic Josephson junction and show that the expected regime is dominated by quantum fluctuations.