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Physical Review A

Strong squeezing by repeated frequency jumps

József Janszky, Петер Адам

Published Nov 1, 1992• 56 citations
Publisher

Abstract

The consequences of sudden frequency changes of a quantum oscillator from ${\mathrm{\ensuremath{\omega}}}_{1}$ to ${\mathrm{\ensuremath{\omega}}}_{2}$ and back is considered. A strong dependence of squeezing on the time interval between the frequency jumps is found. It is shown that a high degree of squeezing can be achieved by a series of sudden frequency changes.

DOI
10.1103/physreva.46.6091

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The consequences of sudden frequency changes of a quantum oscillator from \ensuremathω1{\mathrm{\ensuremath{\omega}}}_{1}\ensuremathω1​ to \ensuremathω2{\mathrm{\ensuremath{\omega}}}_{2}\ensuremathω2​ and back is considered. A strong dependence of squeezing on the time interval between the frequency jumps is found. It is shown that a high degree of squeezing can be achieved by a series of sudden frequency changes.
It is shown that squeezing will inevitably be generated in a harmonic oscillator with time-dependent frequency for any nonvanishing rate of frequency change, sudden or smooth. The general form of the time-dependent transition probabilities among the eigenstates of the initial Hamiltonian is obtained with an exact operator approach. Results for the case of a sudden frequency jump are explicitly given as an illustration. It is also pointed out that to generate squeezing in a harmonic oscillator, the Hamiltonian does not have to be a unitary squeeze transformation of the free Hamiltonian.
The theoretical basis of a mechanism for squeezing through a frequency jump of a harmonic oscillator is examined. It is found that a related squeezing transformation exists, but its interpretation in terms of a frequency change is not possible. A reinterpretation of the results in terms of a scaling transformation in coordinate or momentum variables is given. Moreover, a sudden jump is not essential, and squeezing can evolve continuously. The equations of motion for such a process are obtained and the interaction responsible for squeezing is obtained.
The problem of quantum harmonic oscillator with time-dependent frequency has been solved analytically only for special co(t) functions. In this paper (Sec. 1.) we give a recursive method to determine the creation and annihilation operators for any step-like 0)(0 (t) functions (i. e. functions being constant between jumps). In Sec. 2. we apply this method to jumps between two values of w. In Sec 3. we approximate more general functions with a series of small jumps, we examine the Fourier series of the function defined in Sec. 2, and show that even the first Fourier component leads to increasing squeezing.
Quantum sensing and quantum information processing use quantum advantages such as squeezed states that encode a quantity of interest with higher precision and generate quantum correlations to outperform classical methods. In harmonic oscillators, the rate of generating squeezing is set by a quantum speed limit. Therefore, the degree to which a quantum advantage can be used in practice is limited by the time needed to create the state relative to the rate of unavoidable decoherence. Alternatively, a sudden change of harmonic oscillator's frequency projects a ground state into a squeezed state which can circumvent the time constraint. Here, we create squeezed states of atomic motion by sudden changes of the harmonic oscillation frequency of atoms in an optical lattice. Building on this protocol, we demonstrate rapid quantum amplification of a displacement operator that could be used for detecting motion. Our results can speed up quantum gates and enable quantum sensing and quantum information processing in noisy environments.