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Physical Review A

Quantum-statistical properties of a particle in a double-harmonic-oscillator potential: Generation of Schrödinger-cat states

G. V. Varada, G. S. Agarwal

Published Dec 1, 1993• 23 citations
Publisher

Abstract

The quantum-mechanical double harmonic oscillator is proposed as a model for the generation of Schr\"odinger-cat states. To demonstrate this the quantum-statistical properties of the double oscillator in its ground state are examined. The nonclassical nature of this state and interference effects are analyzed. The squeezing properties of the double harmonic oscillator are calculated and compared with those of the ``idealized'' cat state. The behavior of the quasiprobability distribution function is also discussed.

DOI
10.1103/physreva.48.4062

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The quantum-mechanical double harmonic oscillator is proposed as a model for the generation of Schr"odinger-cat states. To demonstrate this the quantum-statistical properties of the double oscillator in its ground state are examined. The nonclassical nature of this state and interference effects are analyzed. The squeezing properties of the double harmonic oscillator are calculated and compared with those of the ``idealized'' cat state. The behavior of the quasiprobability distribution function is also discussed.
The two-mode even and odd coherent Schrödinger cat states are introduced for the generalized stationary and non-stationary harmonic oscillator. The expected values of positions and momenta and their dispersion matrices are calculated for the Schrödinger cat states. The quadrature squeezing and correlation phenomenon are studied and the Wigner and Husimi functions are constructed explicitly for these states. The photon statistics of the two-mode even and odd coherent states of the generalized oscillator is described in terms of the photon distribution function, which is expressed in terms of Hermite polynomials. The photon number, means and dispersions show oscillations which are characteristics of squeezing and correlation phenomenon.
We consider a system composed of a two-level system (i.e., a qubit) and a harmonic oscillator in the ultrastrong-coupling regime, where the coupling strength is comparable to the qubit and oscillator energy scales. Special emphasis is placed on the possibility of preparing nonclassical states in this system. These nonclassical states include squeezed states, Schr\"odinger-cat states, and entangled states. We start by comparing the predictions of a number of analytical methods that can be used to describe the system under different assumptions, thus analyzing the properties of the system in various parameter regimes. We then examine the ground state of the system and analyze its nonclassical properties. We finally discuss some questions related to the possible experimental observation of the nonclassical states and the effect of decoherence.
The concept of a photon added two-mode Schrödinger cat state in which both modes are independent is introduced, and their nonclassical properties and entanglement are studied. The introduced states emerge as eigenstates of f 1 f 2 a 1 a 2 , where f 1 , f 2 are nonlinear functions of the number operator, and a 1 , a 2 are annihilation operators. We study the evolution of these states under canonical transformation using the parity operator for the case of standard coherent states of the harmonic oscillator. The nonclassical properties of these states are evaluated especially by considering sub-Poissonian photon statistics and photon number distribution. Interestingly, the addition of photons leads to shifting the region in which photon number distribution shows oscillatory behavior. In addition, the entanglement of introduced states is quantitatively analyzed using concurrence. We observe that the state approaches maximum entanglement more rapidly after the addition of photons.