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Register a new userSqueezed States and Helmholtz Spectra
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Added by
Francisco Javier Delgado Cepeda
Publication date
1997
fields
Physics
and research's language is
English
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The classical interpretation of the wave function psi(x) reveals an interesting operational aspect of the Helmholtz spectra. It is shown that the traditional Sturm-Liouville problem contains the simplest key to predict the squeezing effect for charged particle states.
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Continuous-variable codes are an expedient solution for quantum information processing and quantum communication involving optical networks. Here we characterize the squeezed comb, a finite superposition of equidistant squeezed coherent states on a line, and its properties as a continuous-variable encoding choice for a logical qubit. The squeezed comb is a realistic approximation to the ideal code proposed by Gottesman, Kitaev, and Preskill [Phys. Rev. A 64, 012310 (2001)], which is fully protected against errors caused by the paradigmatic types of quantum noise in continuous-variable systems: damping and diffusion. This is no longer the case for the code space of finite squeezed combs, and noise robustness depends crucially on the encoding parameters. We analyze finite squeezed comb states in phase space, highlighting their complicated interference features and characterizing their dynamics when exposed to amplitude damping and Gaussian diffusion noise processes. We find that squeezed comb state are more suitable and less error-prone when exposed to damping, which speaks against standard error correction strategies that employ linear amplification to convert damping into easier-to-describe isotropic diffusion noise.
Starting with a thermal squeezed state defined as a conventional thermal state based on an appropriate hamiltonian, we show how an important physical property, the signal-to-noise ratio, is degraded, and propose a simple model of thermalization (Kraus thermalization).
We propose a scheme for generating squeezed states in solid state circuits consisting of a nanomechanical resonator (NMR), a superconducting Cooper-pair box (CPB) and a superconducting transmission line resonator (STLR). The nonlinear interaction between the NMR and the STLR can be implemented by setting the external biased flux of the CPB at certain values. The interaction Hamiltonian between the NMR and the STLR is derived by performing Fr$rmddot o$hlich transformation on the total Hamiltonian of the combined system. Just by adiabatically keeping the CPB at the ground state, we get the standard parametric down-conversion Hamiltonian. The CPB plays the role of ``nonlinear media, and the squeezed states of the NMR can be easily generated in a manner similar to the three-wave mixing in quantum optics. This is the three-wave mixing in a solid-state circuit.
In the framework of Lindblad theory for open quantum systems, we calculate the entropy of a damped quantum harmonic oscillator which is initially in a quasi-free state. The maximally predictable states are identified as those states producing the minimum entropy increase after a long enough time. In general, the states with a squeezing parameter depending on the environments diffusion coefficients and friction constant are singled out, but if the friction constant is much smaller than the oscillators frequency, coherent states (or thermalized coherent states) are obtained as the preferred classical states.
In this doctoral thesis we have studied the quantum properties of several models which have been classified as statical and dynamical systems. The first part has been devoted to investigate the properties of the statical models including the superposition of squeezed displaced number states with and without thermal noise. Also we have developed a new type of multidimensional squeeze operator including two different squeezing mechanisms. In the second part the dynamical models were given to show the interaction between modes in the nonlinear optical coupler.
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