We present a method for calculating the Aharonov-Anandan phase for time-independent Hamiltonians that avoids the calculation of evolution operators. We compare the generic method used to calculate the Aharonov-Anandan phase with the method proposed h
ere through four examples; a spin-1/2 particle in a constant magnetic field, an arbitrary infinite-sized Hamiltonian with two known eigenvalues, a Fabry-Perot cavity with one movable mirror and a three mirrors cavity with a slightly transmissive movable middle mirror.
We consider a small partially reflecting vibrating mirror coupled dispersively to a single optical mode of a high finesse cavity. We show this arrangement can be used to implement quantum squeezing of the mechanically oscillating mirror.
We consider the dynamics of a vibrating and rotating end-mirror of an optical Fabry-P{erot} cavity that can sustain Laguerre-Gaussian modes. We demonstrate theoretically that since the intra-cavity field carries linear as well as angular momentum, ra
diation pressure can create bipartite entanglement between a vibrational and a rotational mode of the mirror. Further we show that the ratio of vibrational and rotational couplings with the radiation field can easily be adjusted experimentally, which makes the generation and detection of entanglement robust to uncertainties in the cavity manufacture. This constitutes the first proposal to demonstrate entanglement between two qualitatively different degrees of freedom of the same macroscopic object.
It has previously been shown theoretically that the exchange of linear momentum between the light field in an optical cavity and a vibrating end mirror can entangle the electromagnetic field with the vibrational motion of that mirror. In this paper w
e consider the rotational analog of this situation and show that radiation torque can similarly entangle a Laguerre-Gaussian cavity mode with a rotating end mirror. We examine the mirror-field entanglement as a function of ambient temperature, radiation detuning and orbital angular momentum carried by the cavity mode.
