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Register a new userEvolution of Fock states in three mixed harmonic oscillators: quantum statistics
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Added by
Faisal El-Orany Dr.
Publication date
2011
fields
Physics
and research's language is
English
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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.
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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.
Quantum simulations are becoming an essential tool for studying complex phenomena, e.g. quantum topology, quantum information transfer, and relativistic wave equations, beyond the limitations of analytical computations and experimental observations. To date, the primary resources used in proof-of-principle experiments are collections of qubits, coherent states or multiple single-particle Fock states. Here we show the first quantum simulation performed using genuine higher-order Fock states, with two or more indistinguishable particles occupying the same bosonic mode. This was implemented by interfering pairs of Fock states with up to five photons on an interferometer, and measuring the output states with photon-number-resolving detectors. Already this resource-efficient demonstration reveals new topological matter, simulates non-linear systems and elucidates a perfect quantum transfer mechanism which can be used to transport Majorana fermions.
In this paper we introduce a new method for constructing coherent states for 2D harmonic oscillators. In particular, we focus on both the isotropic and commensurate anisotropic instances of the 2D harmonic oscillator. We define a new set of ladder operators for the 2D system as a linear combination of the x and y ladder operators and construct the $SU(2)$ coherent states, where these are then used as the basis of expansion for Schrodinger-type coherent states of the 2D oscillators. We discuss the uncertainty relations for the new states and study the behaviour of their probability density functions in configuration space.
In d-dimensional lattices of coupled quantum harmonic oscillators, we analyze the heat current caused by two thermal baths of different temperature, which are coupled to opposite ends of the lattice, with focus on the validity of Fouriers law of heat conduction. We provide analytical solutions of the heat current through the quantum system in the non-equilibrium steady state using the rotating-wave approximation and bath interactions described by a master equation of Lindblad form. The influence of local dephasing in the transition of ballistic to diffusive transport is investigated.
The quantum harmonic oscillator (QHO), one of the most important and ubiquitous model systems in quantum mechanics, features equally spaced energy levels or eigenstates. Here we report on the design, demonstration and operation of nearly perfect QHOs in AlGaAs/GaAs heterostructure. On the basis of model calculations, we demonstrate that, when a substitutional Si donor substitutes the Ga/Al lattice site close to AlGaAs/GaAs heterointerface, a hydrogenic Si QHO, characterized by a restoring Coulomb force producing square law harmonic potential, is formed. This gives rise to QHO states with energy spacing of ~8-9 meV. We experimentally confirm this proposal by utilizing Stark effect and measuring QHO states using an aluminum single-electron transistor (SET). A sharp and fast oscillation with period of ~7-8 mV appears in addition to the regular Coulomb blockade (CB) oscillation with much larger period, for positive gate biases above 0.5 V. The observation of fast oscillation and its behavior is qualitatively consistent with our theoretical result, manifesting the harmonic motion of electrons from the QHO. Our results might establish a general principle to design, construct and manipulate QHOs in semiconductor heterostructures.
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