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Mysteries, Puzzles, and Paradoxes in Quantum Mechanics

“Parity effect” based generation of Schrodinger cat like states in high-

Anna Napoli, ANTONINO MESSINA

Published Jan 1, 1999• 1 citation
Publisher

Abstract

It has been very recently shown that the dynamics of a two-level atom coupled to a bimodal degenerate cavity field by two-photon processes, is characterized by an interesting nonclassical dynamical behavior christened “parity effect”. This effect consists in the fact that if the cavity field is prepared leaving one mode in its vacuum state and exciting the other one in a generic linear combination of even number states only, or odd number states only, then there exists an appropriate intensity-dependent interval of time after which the bimodal cavity exhibits macroscopically different parity-dependent quantum features. We show that this nonclassical effect is at the origin of the possibility of generating Schrodinger cat like states of the bimodal field appropriately selecting its initial conditions.

DOI
10.1063/1.57865

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It has been very recently shown that the dynamics of a two-level atom coupled to a bimodal degenerate cavity field by two-photon processes, is characterized by an interesting nonclassical dynamical behavior christened “parity effect”. This effect consists in the fact that if the cavity field is prepared leaving one mode in its vacuum state and exciting the other one in a generic linear combination of even number states only, or odd number states only, then there exists an appropriate intensity-dependent interval of time after which the bimodal cavity exhibits macroscopically different parity-dependent quantum features. We show that this nonclassical effect is at the origin of the possibility of generating Schrodinger cat like states of the bimodal field appropriately selecting its initial conditions.
We introduce a new solvable effective Hamiltonian model describing a two-level atom coupled to a bimodal degenerate cavity field by two-photon processes. We study the evolution of the system assuming the atom and one mode in their respective ground states and the other mode in an excited Fock state. We find that the dynamics of the system displays nonclassical behaviour exhibiting, in particular, a peculiar sensitivity to the parity of the initial number of photons. We show that this quantum effect may be exploited to generate the amplification of an initially given small difference in the mode populations also enabling the preparation of quantum superpositions of macroscopically distinct field states.
The rapidly increasing capability to modulate the physicochemical properties of atomic groups and molecules by means of their coupling to radiation, as well as the revolutionary potential of quantum computing for materials simulation and prediction, fuel the interest for non-classical phenomena produced by atom-radiation interaction in confined space. One of such phenomena is a “parity effect” that arises in the dynamics of an atom coupled to two degenerate cavity field modes by two-photon processes and manifests itself as a strong dependence of the field dynamics on the parity of the initial number of photons. Here we identify the physical origin of this effect in the quantum correlations that produce entanglement among the system components, explaining why the system evolution depends critically on the parity of the total number of photons. Understanding the physical underpinnings of the effect also allows us to characterize it within the framework of quantum information theory and to generalize it. Since a single photon addition/removal has dramatic effects on the system behavior, this effect may be usefully applied, also for amplification purposes, to optoelectronics and quantum information processing.
A new conditional scheme for entangling the two quantized modes of a bimodal high-Q cavity field is presented. We show that, injecting one at time k atoms inside the cavity, it is possible to guide the field toward k-dependent linear combinations of k + 1 bimodal Fock states, each one possessing the same total number of photons. The two simple cases corresponding to the passage of one or two atoms only through the resonator are considered. Their practical feasibility against cavity losses, spontaneous emission and other sources of imprecision of the experimental set-up is discussed. Two examples illustrating the usefulness of and the interest toward the creation of such a local entanglement, are reported. The first one relates the specific features of these bimodal entangled states to the occurrence of a non-classical correlation effect in the dynamics of a two-level atom interacting with the entangled cavity. The second one demonstrates that the peculiar entanglement initially stored in the cavity in accordance with our method, provides an effectively exploitable resource to entangle two spatially separated cavities.
The one-atom laser based on electromagnetically induced transparency, suggested recently [ Phys. Rev. Lett. 124 , 093603 ( 2020 ) PRLTAO 0031-9007 10.1103/PhysRevLett.124.093603 ], is capable of generating Schrödinger cat states in the regime of strong ground-state coupling. In this regime, we find the exact solution for the Schrödinger equation with a time-dependent effective Hamiltonian by considering the Magnus expansion of the time-ordered exponential and calculating analytically the time-ordering terms, omitted in the previous study. We show that the time-ordering term affects the relative phase of two coherent components of the generated Schrödinger cat state. We show this influence by calculating various nonclassicality indicators for the cavity field, such as total noise, average parity, and relative total noise. We find that time-ordering becomes important at the average photon number in the cavity below 1, in striking contrast to the case of single-pass parametric downconversion, where it becomes important at average photon number in one optical mode above 4.
We investigate the quantum evolution of the pump field in second-harmonic generation under strong pump depletion. Starting from a coherent state, the pump develops a nonclassical phase-space structure resembling a Schrödinger cat state. This behavior originates from phase instability induced by vacuum fluctuations of the harmonic mode. A rigorous quantum analysis has been performed for mean photon numbers up to ⟨n^⟩=100\langle \hat n \rangle = 100⟨n^⟩=100 in pump mode. For larger photon numbers, up to ⟨n^⟩=107\langle \hat n \rangle = 10^{7}⟨n^⟩=107, the dynamics have been analyzed using a classical trajectory method with sampled initial conditions that reproduces the main features of the quantum evolution. The results indicate that nonlinear frequency conversion can generate macroscopic superposition-like states of the pump field. Although the resulting state is not pure due to correlations with the second-harmonic wave, it remains non-classical with negative zones of Wigner function. These results indicate that strongly nonlinear frequency conversion can provide a scalable route toward macroscopic nonclassical states of light.