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Journal of Modern Optics

Production of Macroscopic Schrödinger Cat States from Weak Quantized Cavity Fields Interacting with Atoms Driven by Classical Fields

Vladimír Bužek, Ts. Gantsog, M.S. Kim

Published Aug 1, 1994• 1 citation
Publisher

Abstract

We show that macroscopic superposition (Schrödinger cat) states of a quantized single-mode cavity field can be produced via the interaction of this field with a two-level atom which is driven by a classical field even for small initial intensities of the quantized cavity mode. We show that with a properly chosen driving field an almost pure superposition state with arbitrary amplitudes and phases of component states can be produced.

DOI
10.1080/09500349414552461

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We show that macroscopic superposition (Schrödinger cat) states of a quantized single-mode cavity field can be produced via the interaction of this field with a two-level atom which is driven by a classical field even for small initial intensities of the quantized cavity mode. We show that with a properly chosen driving field an almost pure superposition state with arbitrary amplitudes and phases of component states can be produced.
We show that the resonant interaction between a two-level atom and a quantized field mode via two-photon transitions leads to extreme quantum entanglement between the atom and quantum field. Nevertheless during the time evolution there are moments at which the atom-field system becomes asymptotically disentangled. We investigate statistical properties of the pure-field states generated at such times. We show that at the quarter of the revival time the field is produced in the pure superposition state (Schrödinger cat state) composed of two coherent states with the same amplitude but which are out of phase by 90° (we obtain approximate analytical solution for this superposition state). We show that the interference between component states leads to non-classical oscillations in the photon number distribution. At the revival time the field is again in the pure state (we present an approximate analytical solution for the corresponding state vector). This pure state is not a superposition state. Nevertheless it exhibits a certain degree of sub-Poissonian photon statistics. We briefly discuss the influence of the Stark shift on the production of superposition states.
A simple method is presented for generating multicomponent Schrödinger cat states through resonant atom-field interactions. In the scheme n two-level atoms, initially in ground states, are sent through a resonant cavity filled with a strong coherent field sequentially. Then state-selective measurements are performed on the atoms. The detections of the atoms in ground states collapse the cavity field onto a superposition of 2 n coherent states. This is the first way for producing superpositions of many coherent states through resonant atom-field interaction.
Based on the measurement of charge states, we show that the superpositions of two macroscopically distinguishable coherent states (Schr\\"odinger cat states) of a single-mode cavity field can be generated by a controllable interaction between a cavity field and a SQUID-based charge qubit. After such cat states of the cavity field are created, the interaction can be switched off by the classical magnetic field through the SQUID, and there is no information transfer between the cavity field and the charge qubit. We also discuss the generation of superpositions of two squeezed coherent states.
Schr\odinger cat states of photons can be prepared by effective gauge fields gated by the quantum states of a two-level atom interacting with three cavities. By periodically modulating the cavity frequencies with different phases, opposite effective gauge fields of cavity photons can be created for the two quantum states of the atom. A superposition of atomic states can transport photons from one cavity to a macroscopic superposition of the other two cavities. This mechanism provides new possibilities in exploring quantum entanglement and has applications in quantum metrology and quantum information.
In 1935, Erwin Schrödinger put forward his famous gedanken experiment in which a microscopic degree of freedom - the emission state of a radioactive atom - and a macroscopic, classical state - the life or death of a cat - are entangled [1]. The resulting state is dubbed a Schrodinger-cat state. According to quantum theory, a measurement of the atom in a superposition basis projects the cat into a macroscopic superposition of being alive and dead. Here, we use coherent laser fields with different optical phases as a macroscopic model system and generate entangled Schrodinger-cat states in a deterministic way [3]. We reflect the coherent pulses from an optical cavity that contains a single strongly-coupled atom. This entangles the spin of the atom with the optical phase of the light field [2]. By manipulating and detecting the atomic state, we create a plethora of flying optical coherent-state superpositions. We reconstruct the corresponding Wigner functions (see Fig. 1) to demonstrate the tunability and non-classicality of the produced light state.
We study the dynamics of the Jaynes–Cummings model for two two-level systems (or qubits) interacting with a quantized single mode electromagnetic cavity (or quantum bus), extending this to the macroscopic case of an array of Nq qubits. For an initial cavity coherent state |α⟩ and the qubit system in a specified “basin of attraction” in its Hilbert space, we demonstrate the oscillation of a superposition of two macroscopic quantum states between the qubit system and the field mode. From the perspective of either the qubit or the field system, there is collapse and revival of a “Schrödinger cat” state.