Multimode States Research Articles

Generalized multimode squeezed states.

The notion of squeezing is generalized to the case of multimodes. The multimode generalized squeezing operator has similar algebraic properties to those of the single-mode case and reduces to the usual two-mode squeezing operator in the case of two modes. It is also shown that the generalized multimode squeezed state is a multimode minimum-uncertainty state if the squeezing parameters are real.

The Evolution of Correlations in a Dissipative System

Abstract We examine the decay of two correlated atoms to a reservoir prepared in its ground state and in a squeezed multimode vacuum state. We calculate the entropies for the atoms and use the index of correlation to show the decay and regeneration of correlations between the atoms as they interact with the reservoir.

Rigged-reservoir response II Effects of a squeezed vacuum

As a specific example of the linear response induced by a rigged reservoir, we construct one from an assembly of harmonic oscillators in a multimode squeezed state. In the rotating frame of the boson mode the squeezed reservoir offers noise properties corresponding to those characterizing a stationary random process. With a squeezed reservoir an attenuator can produce a squeezed output, irrespective of its input. For an arbitrarily squeezed reservoir the amplifier can provide a squeezed output for a gain even larger than 2, thus beating the cloning limit.

Intermodal stability of a coupled-cavity semiconductor laser

We present an analysis of the steady-state operation of a two-element coupled-cavity laser near a mode hop. The equations of motion for the two cavities and two relevant modes of a longitudinally coupled-cavity laser are reduced to a system of nondimensional nonlinear ordinary differential equations which describe a general two-element laser. The equations are then solved and the stability of their solutions is analyzed. Depending upon the fill factors for the two modes, there exists an intrinsically multimode oscillation for operating conditions under which it was previously thought that no steady state existed. Under conditions where the multimode state is unstable, both of the single-mode states are stable with bistable transitions occurring only on the boundaries of the unstable multimode regimes.

Phase and amplitude uncertainties in heterodyne detection

The quantum limits on simultaneous phase and squared-amplitude measurements made via optical heterodyne detection on a single-mode radiation field are established. The analysis proceeds from a fully quantum mechanical treatment of heterodyning with ideal photon detectors. A high mean field uncertainty principle is proven for simultaneous phase and squared-amplitude observations under the condition that the signal and image band states are independent, and the image band has zero mean. Operator representations are developed which show that no such principle applies when arbitrary signal/image band dependence is permitted, although the mean observations are no longer functions of the signal field alone. A multimode two-photon coherent state illustrating this behavior at finite energy is exhibited. Potential applications for the resulting improved accuracy measurements are briefly described.

The derivation of a cluster model for the optical absorption spectrum of strongly coupled Jahn-Teller systems

The single-frequency cluster model for the Jahn-Teller effect and the multimode model for an arbitrary phonon spectrum are shown to give the same low-temperature optical absorption spectrum in the limit of strong coupling for a variety of different Jahn-Teller systems. This result will be of considerable value in the interpretation of band shapes because of the practical difficulty of calculating multimode band shapes directly. The parameters of the cluster model appropriate for the optical spectrum differ from those previously given for the description of the multimode ground state.

Classical-quantum correspondence for multilevel systems

The properties of $r$-mode harmonic-oscillator coherent states are reviewed. In particular, the $\mathcal{D}$-algebra differential-operator realization of the creation and annihilation operators on the coherent states and their diagonal projectors is constructed. A homomorphism between the algebra describing $r$-field modes and the algebra describing $r$-level systems is exhibited explicitly. This homomorphism allows the projection of the multimode calculus onto the multilevel calculus. In particular, multimode coherent states and projectors can be used as generating functions for multilevel coherent states and projectors. In addition, the multilevel $\mathcal{D}$ algebra is constructed directly from the multimode $\mathcal{D}$ algebra under this homomorphism. For illustrative purposes, the $\mathcal{D}$ algebra for the diagonal coherent-state projectors for two-level atomic systems is presented explicitly in terms of a parametrization in the Bloch angles $\ensuremath{\theta}$ and $\ensuremath{\phi}$. Two classes of applications are treated: (a) the mapping of atomic-density-operator equations of motion into phase-space equations of motion for the quasiprobability weighting function $P$; (b) the construction of equations of motion for the diagonal elements $Q$ of the density operator in the coherent states. It is shown that the solution to either equation with the appropriate initial condition gives complete statistical information for the atomic system. It is shown explicitly that the functions $P$ and $Q$ are related by a convolution integral.