Coherent states in Finite Quantum Mechanics

J. Tolar, Goce Chadzitaskos

Finite-dimensional quantum mechanics (quantum mechanics on finite discrete space - the cyclic group of order M) is developed further: in analogy with the usual harmonic oscillator coherent states, an overcomplete family of coherent states over the phase space is constructed and their properties are determined.

Alfred Wünsche, V. V. Dodonov, Olga V. Man’ko +1 more

The nearest Hilbert-Schmidt distance of (pure) states to coherent states is discussed as a quantitative measure of nonclassicality of states in quantum optics or quantum mechanics of harmonic oscillators. Fock states, squeezed coherent states and finite superpositions of coherent states (Schrödinger cat states) are considered as examples. Some other approaches to nonclassicality of states in quantum optics are shortly discussed.

George A. Hagedorn

Dušan Popov

Since, unlike “traditional” physics, computational physics uses the discretization formalism, in this paper we have focused our attention on the discrete approach in order to solve the Schrödinger as well as the Bloch equations for a free particle and the “quantum gas” of free particles in an infinite quantum well with the finite length, respectively. By applying the so called continuous quantum mechanics limit we recover the corresponding results in continuous-variable quantum mechanics. For the infinite quantum well model we formulated the associated coherent states, which lead to the expression for the coherent qubits, in counterpart to the thermal qubits, obtained as a result of using the thermofield dynamics model. Thus, a “bridge” is created between the infinite quantum well model, coherent states and thermofield dynamics, which ultimately converge towards Quantum Computing.