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Optics and Spectroscopy

Rabi oscillations in the dynamics of a fully quantized SQUID ring-electromagnetic field system

Rosanna Migliore, ANTONINO MESSINA

Published May 1, 2003• 3 citations
Publisher

Abstract

In this paper, a study based on a fully quantum-mechanical model for the coupling between a super-conducting quantum interference device (an rf SQUID) and a single-mode quantized electromagnetic field is presented. The aim of this work is the prediction of the existence of some interesting phenomena, characterized by more than one Rabi frequency, occurring in the dynamics of the total coupled system when our analysis is developed inside a reduced low-lying energy 4D Hilbert subspace.

DOI
10.1134/1.1576858

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In this paper, a study based on a fully quantum-mechanical model for the coupling between a super-conducting quantum interference device (an rf SQUID) and a single-mode quantized electromagnetic field is presented. The aim of this work is the prediction of the existence of some interesting phenomena, characterized by more than one Rabi frequency, occurring in the dynamics of the total coupled system when our analysis is developed inside a reduced low-lying energy 4D Hilbert subspace.
In this paper we investigate the dynamical behavior of a SQUID ring coupled to a quantized single-mode electromagnetic field. We have calculated the eigenstates of the combined fully quantum mechanical SQUID-field system. Interesting phenomena occur when the energy difference between the usual symmetric and anti-symmetric SQUID states equals the field energy ℏωF. We find the low-energy lying entangled stationary states of the system and demonstrate that its dynamics is dominated by coherent Rabi oscillations.
The dynamical behavior of a superconducting quantum interference device (an rf-SQUID) irradiated by a single-mode quantized electromagnetic field is theoretically investigated. Treating the SQUID as a flux qubit, we analyze the dynamics of the combined system within the low-lying energy Hilbert subspace both in the asymmetric and in the symmetric SQUID potential configurations. We show that the temporal evolution of the system is dominated by an oscillatory behavior characterized by more than one, generally speaking, incommensurable Rabi frequencies whose expressions are explicitly given. We find that the external parameters may be fixed in such a way to realize a control on the dynamical replay of the total system which, for instance, may be forced to exhibit a periodic evolution accompanied by the occurrence of an oscillatory disappearance of entanglement between the two subsystems. We demonstrate the possibility of generating quantum maximally entangled superpositions of the two macroscopically distinguishable states describing clockwise and counterclockwise supercurrents in the loop. The experimental feasibility of our proposal is briefly discussed.
A quantum system comprising of a monochromatic electromagnetic field coupled to a superconducting quantum interference device (SQUID) ring with sinusoidal nonlinearity is studied. A magnetostatic flux ${\ensuremath{\Phi}}_{x}$ is also threading the SQUID ring, and is used to control the coupling between the two systems. It is shown that for special values of ${\ensuremath{\Phi}}_{x}$ the system is strongly coupled. The time evolution of the system is studied. It is shown that exchange of energy takes place between the two modes and that the system becomes entangled. A second quasiclassical model that treats the electromagnetic field classically is also studied. A comparison between the fully quantum-mechanical model with the electromagnetic field initially in a coherent state and the quasiclassical model is made.
In this paper we consider the interaction of a quantum-mechanical superconducting quantum interference device (SQUID) with a classical monochromatic electromagnetic (EM) field. We solve the time-dependent Schrödinger equation for the SQUID ring in this EM field. We demonstrate that non-perturbative transitions between the low-lying states of the ring, due to coherent multiphoton absorption processes, dominate, even when the single-photon energy is small compared with the energy separation between these states. We present experimental data on small-capacitance SQUID rings, interacting with microwave fields, which point to the existence of such non-perturbative transitions.
We study electromagnetically induced interference at superconducting qubits. The interaction between qubits and electromagnetic fields can provide additional coupling channels to qubit states, leading to quantum interference in a microwave driven qubit. In particular, the interwell relaxation or Rabi oscillation, resulting respectively from the multi- or single-mode interaction, can induce effective crossovers. The environment is modeled by a multi-mode thermal bath, generating the interwell relaxation. Relaxation induced interference, independent of the tunnel coupling, provides deeper understanding to the interaction between the qubits and their environment. It also supplies a useful tool to characterize the relaxation strength as well as the characteristic frequency of the bath. In addition, we demonstrate the relaxation can generate population inversion in a strongly driving two-level system. On the other hand, different from Rabi oscillation, Rabi oscillation induced interference involves more complicated and modulated photon exchange thus offers an alternative means to manipulate the qubit, with more controllable parameters including the strength and position of the tunnel coupling. It also provides a testing ground for exploring nonlinear quantum phenomena and quantum state manipulation, in not only the flux qubit but also the systems with no crossover structure, e.g. phase qubits.
In this paper we investigate the behavior of a fully quantum mechanical system consisting of a mesoscopic SQUID ring coupled to one or two electromagnetic field modes. We show that we can use a static magnetic flux threading the SQUID ring to control the transfer of energy, the entanglement and the statistical properties of the fields coupled to the ring. We also demonstrate that at, and around, certain values of static flux the effective coupling between the components of the system is large. The position of these regions in static flux is dependent on the energy level structure of the ring and the relative field mode frequencies, In these regions we find that the entanglement of states in the coupled system, and the energy transfer between its components, is strong.