We study the quantum properties of a nanomechanical oscillator via the squeezing of the oscillator amplitude. The static longitudinal compressive force $F_0$ close to a critical value at the Euler buckling instability leads to an anharmonic term in the Hamiltonian and thus the squeezing properties of the nanomechanical oscillator are to be obtained from the Hamiltonian of the form $H= a^†a+β(a^†+a)^4/4$ . This Hamiltonian has no exact solution unlike the other known models of nonlinear interactions of the forms $a^{†2}a^2$ , $(a^†a)^2$ and $a^{\dag4}+a^4-(a^{\dag2}a^2+a^2a^{\dag2})$ previously employed in quantum optics to study squeezing. Here we solve the Schrödinger equation numerically and show that in-phase quadrature gets squeezed for both ground state and coherent states. The squeezing can be controlled by bringing $F_0$ close to or far from the critical value $F_c$ . We further study the effect of the transverse driving force on the squeezing in nanomechanical oscillator.We study the quantum properties of a nanomechanical oscillator via the squeezing of the oscillator amplitude. The static longitudinal compressive force $F_0$ close to a critical value at the Euler buckling instability leads to an anharmonic term in the Hamiltonian and thus the squeezing properties of the nanomechanical oscillator are to be obtained from the Hamiltonian of the form $H= a^†a+β(a^†+a)^4/4$. This Hamiltonian has no exact solution unlike the other known models of nonlinear interactions of the forms $a^{†2}a^2$, $(a^†a)^2$ and $a^{\dag4}+a^4-(a^{\dag2}a^2+a^2a^{\dag2})$ previously employed in quantum optics to study squeezing. Here we solve the Schrödinger equation numerically and show that in-phase quadrature gets squeezed for both ground state and coherent states. The squeezing can be controlled by bringing $F_0$ close to or far from the critical value $F_c$. We further study the effect of the transverse driving force on the squeezing in nanomechanical oscillator.

arXiv:cond-mat/0608621Aug 29, 20060 citations

Squeezing in harmonic oscillators with time-dependent frequencies

Xin Ma, William Rhodes

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.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.

Physical Review AFeb 1, 198971 citations

Quantum Oscillators

A. M. Perelomov

Springer eBooksJan 1, 19860 citations

Quantum Oscillators: General Considerations

Elsevier eBooksJan 1, 19950 citations

We study the quantum properties of a nanomechanical oscillator via the squeezing of the oscillator amplitude. The static longitudinal compressive force

F_0

close to a critical value at the Euler buckling instability leads to an anharmonic term in the Hamiltonian and thus the squeezing properties of the nanomechanical oscillator are to be obtained from the Hamiltonian of the form

H= a^†a+β(a^†+a)^4/4

. This Hamiltonian has no exact solution unlike the other known models of nonlinear interactions of the forms

a^{†2}a^2

(a^†a)^2

and

a^{\dag4}+a^4-(a^{\dag2}a^2+a^2a^{\dag2})

previously employed in quantum optics to study squeezing. Here we solve the Schrödinger equation numerically and show that in-phase quadrature gets squeezed for both ground state and coherent states. The squeezing can be controlled by bringing

F_0

close to or far from the critical value

F_c

. We further study the effect of the transverse driving force on the squeezing in nanomechanical oscillator.