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Register a new userManipulating Fock states of a harmonic oscillator while preserving its linearity
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We present a new scheme for controlling the quantum state of a harmonic oscillator by coupling it to an anharmonic multilevel system (MLS) with first to second excited state transition frequency on-resonance with the oscillator. In this scheme that we call ef-resonant, the spurious oscillator Kerr non-linearity inherited from the MLS is very small, while its Fock states can still be selectively addressed via an MLS transition at a frequency that depends on the number of photons. We implement this concept in a circuit-QED setup with a microwave 3D cavity (the oscillator, with frequency 6.4 GHz and quality factor QO=2E-6) embedding a frequency tunable transmon qubit (the MLS). We characterize the system spectroscopically and demonstrate selective addressing of Fock states and a Kerr non-linearity below 350 Hz. At times much longer than the transmon coherence times, a non-linear cavity response with driving power is also observed and explained.
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We show that in the case of unknown {em harmonic oscillator coherent states} it is possible to achieve what we call {it perfect information cloning}. By this we mean that it is still possible to make arbitrary number of copies of a state which has {it exactly} the same information content as the original unknown coherent state. By making use of this {it perfect information cloning} it would be possible to estimate the original state through measurements and make arbitrary number of copies of the estimator. We define the notion of a {em Measurement Fidelity}. We show that this information cloning gives rise, in the case of $1to N$, to a {em distribution} of {em measurement fidelities} whose average value is ${1over 2}$ irrespective of the number of copies originally made. Generalisations of this to the $Mto MN$ case as well as the measurement fidelities for Gaussian cloners are also given.
We have withdrawn this paper due to a fatal flaw in eqn(38).
In this communication we investigate the quantum statistics of three harmonic oscillators mutually interacting with each other considering the modes are initially in Fock states. After solving the equations of motion, the squeezing phenomenon, sub-Poissonian statistics and quasiprobability functions are discussed. We demonstrate that the interaction is able to produce squeezing of different types. We show also that certain types of Fock states can evolve in this interaction into thermal state and squeezed thermal state governed by the interaction parameters.
The solution of the Feinberg-Horodecki (FH) equation for a time-dependent mass (TDM) harmonic oscillator quantum system is studied. A certain interaction is applied to a mass to provide a particular spectrum of stationary energies. The related spectrum of the harmonic oscillator potential acting on the TDM oscillators is found. We apply the time version of the asymptotic iteration method (AIM) to calculate analytical expressions of the TDM stationary state energies and their wave functions. It is shown that the obtained solutions reduce to those of simple harmonic oscillator as the time-dependent of the mass reduces to
We consider a thermal quantum harmonic oscillator weakly coupled to a heat bath at a different temperature. We analytically study the quantum heat exchange statistics between the two systems using the quantum-optical master equation. We exactly compute the characteristic function of the heat distribution and show that it verifies the Jarzynski-Wojcik fluctuation theorem. We further evaluate the heat probability density in the limit of long thermalization times, both in the low and high temperature regimes, and investigate its time evolution by calculating its first two cumulants.
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