A note on squeezing due to sudden change of mass

B. Baseia, A. L. De Brito, Vanderlei Salvador Bagnato

Published Feb 1, 1993• 0 citations

Abstract

A Hilbert space of an harmonic oscillator is spanned into an over complete set of coherent states of another oscillator having different mass to show that a sudden change of mass of a quantum oscillator [e.g., due to mass emission in radiative processes] leads to squeezing. The correspondence of such oscillators with the radiation field is also considered. 12 refs.

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Comment on ‘‘Squeezing and antisqueezing for a harmonic oscillator having a sudden change of mass’’

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It is shown that, contrary to the conclusions of a paper by Baseia, De Brito, and Bagnato [Phys. Rev. A 45, 5308 (1992)], a harmonic oscillator can be squeezed by consecutive sudden changes of its mass to and back.

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A note on squeezing due to sudden change of mass

B. Baseia, A. L. De Brito, Vanderlei Salvador Bagnato

Published Feb 1, 1993• 0 citations

OpenAlex

Abstract

Related papers

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B. Baseia, A. L. De Brito, Vanderlei Salvador Bagnato

Physical Review AApr 1, 199219 citations

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The Hilbert space of a harmonic oscillator with frequency ω can be spanned by the overcomplete set of coherent states of a second oscillator with frequency ω'. These states are squeezed states of the first oscillator. We examine the possibility of generating squeezed states out of coherent states by external changes of the oscillator frequency and explore the two limiting cases of an adiabatic and a sudden change. Only the latter results in squeezing, while in the former symmetrical uncertainities in coordinate and momentum turn out to be adiabatic invariants.The Hilbert space of a harmonic oscillator with frequency ω can be spanned by the overcomplete set of coherent states of a second oscillator with frequency ω'. These states are squeezed states of the first oscillator. We examine the possibility of generating squeezed states out of coherent states by external changes of the oscillator frequency and explore the two limiting cases of an adiabatic and a sudden change. Only the latter results in squeezing, while in the former symmetrical uncertainities in coordinate and momentum turn out to be adiabatic invariants.

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The Kanai-Caldirola (Bateman) Hamiltonian is used to derive the dynamics of a simple harmonic oscillator, initially in a minimum uncertainty state, under the influence of an external agency which causes the mass parameter to change from ${\mathit{M}}_{0}$ to ${\mathit{M}}_{1}$ in a short time \ensuremath{\epsilon}. Then the frequency changes from ${\mathrm{\ensuremath{\omega}}}_{0}$ to ${\mathrm{\ensuremath{\omega}}}_{1}$=( ${\mathit{M}}_{0}$ / ${\mathit{M}}_{1}$ )${\mathrm{\ensuremath{\omega}}}_{0}$+O(${\mathrm{\ensuremath{\epsilon}}}^{2}$). In the limit \ensuremath{\epsilon}\ensuremath{\rightarrow}0, no squeezing or loss of coherence occurs. If ${\mathit{M}}_{1}$ / ${\mathit{M}}_{0}$ =1\ifmmode\pm\else\textpm\fi{}\ensuremath{\eta} (0\ensuremath{\ll}1), then a squeezing of order ${\mathrm{\ensuremath{\epsilon}}}^{2}$\ensuremath{\eta} occurs. If ${\mathit{M}}_{1}$ / ${\mathit{M}}_{0}$ is appreciably different from unity, then the quadrature variances are unequal but the state no longer has minimum uncertainty. An application could be made in quantum optics.The Kanai-Caldirola (Bateman) Hamiltonian is used to derive the dynamics of a simple harmonic oscillator, initially in a minimum uncertainty state, under the influence of an external agency which causes the mass parameter to change from ${\mathit{M}}_{0}$ to ${\mathit{M}}_{1}$ in a short time \ensuremath{\epsilon}. Then the frequency changes from ${\mathrm{\ensuremath{\omega}}}_{0}$ to ${\mathrm{\ensuremath{\omega}}}_{1}$=(${\mathit{M}}_{0}$/${\mathit{M}}_{1}$)${\mathrm{\ensuremath{\omega}}}_{0}$+O(${\mathrm{\ensuremath{\epsilon}}}^{2}$). In the limit \ensuremath{\epsilon}\ensuremath{\rightarrow}0, no squeezing or loss of coherence occurs. If ${\mathit{M}}_{1}$/${\mathit{M}}_{0}$=1\ifmmode\pm\else\textpm\fi{}\ensuremath{\eta} (0\ensuremath{\ll}1), then a squeezing of order ${\mathrm{\ensuremath{\epsilon}}}^{2}$\ensuremath{\eta} occurs. If ${\mathit{M}}_{1}$/${\mathit{M}}_{0}$ is appreciably different from unity, then the quadrature variances are unequal but the state no longer has minimum uncertainty. An application could be made in quantum optics.

Physical Review AAug 1, 199318 citations

Harmonic oscillator interaction with squeezed radiation

V. V. Dodonov, Dmitri E. Nikonov

Although the problem of electromagnetic radiation by a quantum harmonic oscillator is considered in textbooks on quantum mechanics, some of its aspects have remained unclear until now. By this, we mean that usually the initial quantum states of both the oscillator and the field are assumed to be characterized by a definite energy level of the oscillator and definite occupation numbers of the field modes. In connection with growing interest in squeezed states, it would be interesting to analyze the general case when the initial states of both subsystems are arbitrary superpositions of energy eigenstates. This problem was considered in other work, where the power of the spontaneous emission was calculated in the case of an arbitrary oscillator's initial state, but the field was initially in a vacuum state. In the present article, we calculate the rate of the oscillator average energy, squeezing, and correlation parameter change under the influence of an arbitrary external radiation field. Some other problems relating to the interaction between quantum particles (atoms) or oscillators where the electromagnetic radiation is an arbitrary (in particular squeezed) state were investigated.Although the problem of electromagnetic radiation by a quantum harmonic oscillator is considered in textbooks on quantum mechanics, some of its aspects have remained unclear until now. By this, we mean that usually the initial quantum states of both the oscillator and the field are assumed to be characterized by a definite energy level of the oscillator and definite occupation numbers of the field modes. In connection with growing interest in squeezed states, it would be interesting to analyze the general case when the initial states of both subsystems are arbitrary superpositions of energy eigenstates. This problem was considered in other work, where the power of the spontaneous emission was calculated in the case of an arbitrary oscillator's initial state, but the field was initially in a vacuum state. In the present article, we calculate the rate of the oscillator average energy, squeezing, and correlation parameter change under the influence of an arbitrary external radiation field. Some other problems relating to the interaction between quantum particles (atoms) or oscillators where the electromagnetic radiation is an arbitrary (in particular squeezed) state were investigated.

Jan 1, 19930 citations

{\mathit{M}}_{0}

{\mathit{M}}_{1}

in a short time \ensuremath{\epsilon}. Then the frequency changes from ${\mathrm{\ensuremath{\omega}}}_{0}$ to ${\mathrm{\ensuremath{\omega}}}_{1}$=(

{\mathit{M}}_{0}

{\mathit{M}}_{1}

)${\mathrm{\ensuremath{\omega}}}_{0}$+O(${\mathrm{\ensuremath{\epsilon}}}^{2}$). In the limit \ensuremath{\epsilon}\ensuremath{\rightarrow}0, no squeezing or loss of coherence occurs. If

{\mathit{M}}_{1}

{\mathit{M}}_{0}

=1\ifmmode\pm\else\textpm\fi{}\ensuremath{\eta} (0\ensuremath{\ll}1), then a squeezing of order ${\mathrm{\ensuremath{\epsilon}}}^{2}$\ensuremath{\eta} occurs. If

{\mathit{M}}_{1}

{\mathit{M}}_{0}

is appreciably different from unity, then the quadrature variances are unequal but the state no longer has minimum uncertainty. An application could be made in quantum optics.