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Journal of Modern Optics

Microwave-induced quantum transitions in a superconducting quantum interference device

R. Whiteman, Terrence D. Clark, Robert J. Prance, Helen Prance, Volker Schöllmann, Jason F. Ralph, M. J. Everitt, J. Diggins

Published Jun 1, 1998• 13 citations
Publisher

Abstract

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.

DOI
10.1080/09500349808230908

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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.
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 modulation of a SQUID ring (a Josephson weak link enclosed by a thick superconducting ring) by an external electromagnetic (em) field for the case where the ring remains adiabatically in its ground state. We demonstrate that very good agreement can be found between experimental modulation data and the results predicted theoretically by solving the time-dependent Schrödinger equation for the ring-em-field system. We also show that the non-linear dynamical coupling between the ring and an external resonant circuit can influence the exact form of the modulation. Again we find consistent agreement between experiment and theory.
We consider the interaction of a quantum mechanical SQUID ring with a classical resonator (a parallel LCLCLC tank circuit). In our model we assume that the evolution of the ring maintains its quantum mechanical nature, even though the circuit to which it is coupled is treated classically. We show that when the SQUID ring is driven by a classical monochromatic microwave source, energy can be transferred between this input and the tank circuit, even when the frequency ratio between them is very large. Essentially, these calculations deal with the coupling between a single macroscopic quantum object (the SQUID ring) and a classical circuit measurement device where due account is taken of the nonperturbative behavior of the ring and the concomitant nonlinear interaction of the ring with this device.
In this paper we study, by analogy with quantum optics, the superconducting quantum interference device (SQUID) ring mediated quantum mechanical interaction of an input electromagnetic field oscillator mode with two or more output oscillator modes at subintegers of the input frequency. We show that through the nonlinearity of the SQUID ring multiphoton downconversion can take place between the input and output modes with the resultant output photons being created in an entangled state. We also demonstrate that the degree of this entanglement can be adjusted by means of a static magnetic flux which controls the strength of the interaction between these modes via the SQUID ring.
We irradiated an rf superconducting quantum interference device qubit with large-amplitude and high-frequency electromagnetic field. Population transitions between macroscopic distinct quantum states due to multiple Landau-Zener transitions at energy-level avoided crossings were observed. The qubit population on the excited states as a function of flux detuning and microwave power exhibits interference patterns. Some features are found in the interference and a model based on rate equations can well address these features.