Scaling of decoherence effects in quantum computers

Abstract

The scaling of decoherence rates with qubit number N is studied for a simple model of a quantum computer in the situation where N is large. The two state qubits are localized around well-separated positions via trapping potentials and vibrational centre of mass motion of the qubits occurs. Coherent one and two qubit gating processes are controlled by external classical fields and facilitated by a cavity mode ancilla. Decoherence due to qubit coupling to a bath of spontaneous modes, cavity decay modes and to the vibrational modes is treated. A non-Markovian treatment of the short time behaviour of the fidelity is presented, and expressions for the characteristic decoherence time scales obtained for the case where the qubit/cavity mode ancilla is in a pure state and the baths are in thermal states. Specific results are given for the case where the cavity mode is in the vacuum state and gating processes are absent and the qubits are in (a) the Hadamard state (b) the GHZ state.     

Multimode Coherent States and HeNe Laser Light

Abstract

Among the quantum optical states of a tremolant optical cavity are multimode coherent states. Such states are also possible in open cavities where the cavity stabilization time is greater than the multimode beat time. In open cavity resonator lasers they reduce the power limiting effects of spectral hole burning and therefore tend to grow at the expense of single mode coherent states.     

Can the kicked top be realized?

Abstract

Collections of identical two-level atoms can give rise to (quantum) chaotic behaviour if non-resonantly coupled to a resonator mode and periodically driven. Observation of such chaos would require a new generation of experiments on microwave superradiance, or optical variants thereof which would exploit the strong coupling characteristic of very small cavities. Similarly, collections of identical three-level atoms non-resonantly coupled to two cavity modes could provide ‘SU(3) laboratories’, capable of realizing the semiclassical and classical limits of SU(3) dynamics, both integrable and chaotic. Some of the more interesting modes of behaviour of such systems are discussed.     

On the Properties of Surface Plasmon Polarization Beam Splitters

Abstract

The transmission and cross-coupling characteristics of a surface-plasmon-based polarization beam splitter with multimode interlay between two polished optical fibre blocks are presented. Through the continuous monitoring of the characteristics as a function of interlay refractive index and wavelength it was found that the device is symmetrical in terms of optical power coupling in the cross direction and asymmetrical in terms of transmission, with respect to input launch direction. The fibre fixed in the metal-coated block has a transverse electric (TE) mode transmission which is independent of the refractive index of interlay. The transmission of the other (uncovered) block shows resonance-type interaction for both TE and transverse magnetic modes owing to evanescent field coupling to the multimode interlay.     

Self-pulsing in a Laser Model with Discrete Gain and Loss

Abstract

A new model of a multimode homogeneously broadened unidirectional ring cavity laser is presented. Gain and loss are modelled as discrete elements taking the form of a thin laser medium of negligible extent and a partially reflecting mirror forming a cavity with a finite round-trip time. In this way, an exact analytic solution to the stability problem of the c.w. state can be obtained. It is shown that a second threshold exists for any mirror transmissivity and, when using a semitransparent mirror, that it can be reached by pumping seven times above laser threshold. Numerical solutions are presented, including periodic, quasi-periodic and chaotic oscillations. Well known mean-field limit self-pulsations are here predicted for any mirror transmissivity and suitable pump parameter, and are shown to be particular cases of a more general class of instabilities involving excitation of one or more cavity modes by Rabi frequency modulation; the resulting dynamics reflect a complex interaction among the excited modes and the Rabi frequency modulation. The present model predicts, in particular, transition to chaos from a frequency locked limit cycle or from a two-dimensional torus.     

Controlling decoherence of a two-level atom in a lossy cavity

Abstract

By use of external periodic driving sources, we demonstrate the possibility of controlling the coherent as well as the decoherent dynamics of a two-level atom placed in a lossy cavity. The control of the coherent dynamics is elucidated for the phenomenon of coherent destruction of tunnelling (CDT), i.e. the coherent dynamics of a driven two-level atom in a quantum superposition state can be brought practically to a complete standstill. We study this phenomenon for different initial preparations of the two-level atom. We then proceed to investigate the decoherence originating from the interaction of the two-level atom with a lossy cavity mode. The loss mechanism is described in terms of a microscopic model that couples the cavity mode to a bath of harmonic field modes. A suitably tuned external cw-laser field applied to the two-level atom slows down considerably the decoherence of the atom. We demonstrate the suppression of decoherence for two opposite initial preparations of the atomic state: a quantum superposition state as well as the ground state. These findings can be used to decrease the influence of decoherence in qubit manipulation processes.     

Interaction between dual cavity modes in a planar photonic microcavity

Abstract

We theoretically study the interaction between dual cavity modes in a planar photonic microcavity structure in the optical communication wavelength range. The merging and splitting of cavity mode is analysed with realistic microcavity structures. The merging of dual cavity resonance into a single cavity resonance is achieved by changing the number of layers between the two cavities. The splitting of single cavity resonance into dual cavity resonance is obtained with an increase in the reflectivity of mirrors in the front and rear side of the microcavity structure. The threshold condition for the merging and splitting of cavity mode is established in terms of structural parameters. The physical origin of the merging of dual cavity modes into a single cavity resonance is discussed in terms of the electric field intensity distribution in the microcavity structure. The microcavity structure with dual cavity modes is useful for the generation of entangled photon pairs, for achieving the strong-coupling regime between exciton and photon and for high-resolution multi-wavelength filters in optical communication.     

Monte Carlo investigation of an atom laser with a modulated quasi-one-dimensional cavity

Abstract

The dynamics of a recently proposed atom laser scheme based on a modulated quasi-one-dimensional atom cavity are investigated. A three-mode model is developed which includes the effects of dipole–dipole collisions as well as pump and loss mechanisms. It is shown that the Monte Carlo wavefunction simulation technique is superior to a direct solution of the resulting master equation because of the existence of constants of motion which are present in the Monte Carlo wavefunctions but not in the full density operator. Under suitable parameter choices, the solution to the master equation leads to Poissonian atom statistics in the occupation of a single-atomic-cavity mode, analogous to the photon statistics of the optical laser. A threshold behaviour is predicted as the losses are varied relative to the gain for the laser mode.     

Quasi mode theory of macroscopic canonical quantization in quantum optics and cavity quantum electrodynamics

Abstract

A macroscopic, canonical quantization of the EM field and radiating atom system in quantum optics and cavity QED involving classical, linear optical devices, based on expanding the vector potential in terms of quasi mode functions is presented. The quasi mode functions approximate the true mode functions for the device, and are obtained by solving the Helmholtz equation for an idealized spatially dependent electric permittivity function describing the device. The Hamiltonian for the EM field and radiating atom system is obtained in multipolar form and the quantum EM field is found to be equivalent to a set of quantum harmonic oscillators, one oscillator per quasi mode. However, unlike true mode theory where the quantum harmonic oscillators are uncoupled, in the quasi mode theory they are coupled and photon exchange processes can occur. Explicit expressions for the coupling constants are obtained. The interaction energy between the radiative atoms and the quantum EM field depends on the amplitudes of the quasi mode functions at the positions of the radiating atoms, similar to that for the true mode approach. The simpler forms for the quasi mode functions enable the atom-field interaction energy to be written in a form in which the atoms are only coupled to certain types of modes—for example cavity quasi modes, which are large inside the optical cavity. In such cases the escape of energy from excited atoms in the cavity can be pictured in quasi mode theory as a two step process—the atom de-excites and creates a photon in a cavity quasi mode, the photon in the cavity quasi mode is then lost and appears as a photon in an external quasi mode. In this process the first step occurs via the atom-cavity quasi mode interaction, the second through coupling between cavity and external quasi modes. This may be contrasted with the true mode approach, where the excited atom loses its energy and the photon is created in one of the true modes. As all true modes have non-zero amplitudes outside as well as inside the cavity, the escape of energy from excited atoms in the cavity is seen as a one step process. An application of the quasi mode theory to the quantum theory of the beam splitter is outlined. The unitary operator used to describe this device is a scattering operator, relating initial and long time values of annihilation, creation operators for pairs of incident and reflected modes, interpreted here as quasi modes.     

Influence of external cavity length on multimode hopping in microchip Nd:YAG lasers

The influence of external cavity length on multimode hopping in microchip Nd:YAG lasers is investigated experimentally. With an optical feedback loop, the threshold gain of different longitudinal modes are all modulated by changing the external cavity length; a lambda/2 change in the external cavity length causes a one-period oscillation. The longitudinal modes can be divided into groups according to different initial threshold gain variations and modulation trends corresponding to different external cavity phases. Because of the initial gain difference, only one mode in each group is the dominant potential lasing mode, while others are suppressed. During the 2 pi change of the external cavity phase, mode hopping occurs among these potential lasing modes from different groups. Both the intensity waveforms and the number of hopping modes strongly depend on the external cavity length. Experimental results agree well with the theoretical analysis of the phenomenon of multimode hopping subjected to optical feedback in microchip Nd:YAG lasers.     

Influence of Kerr-like medium on the dynamics of a two-mode Raman coupled model

Abstract

We study the quantum dynamics of an effective two-level atom interacting with two modes via Raman process inside an ideal cavity in the presence of Kerr non-linearity. The cavity modes interact both with the atom as well as the Kerr-like medium. The unitary transformation method presented here, not only solves the time-dependent problem, but also provides the eigensolutions of the interacting Hamiltonian at the same time. We study the atomic-population dynamics and the dynamics of the photon statistics in the two cavity modes. The influence of the Kerr-like medium on the statistics of the field is explored and it is observed that Kerr medium introduces antibunching in mode 1 and this effect is enhanced by a stronger interaction with the non-linear medium. In the high non-linear coupling regime anticorrelated beam become correlated. Kerr medium also introduces non-classical correlation between the two modes.     

Quantum state entanglement and readout of collective atomic-ensemble modes and optical wave packets by stimulated Raman scattering

Abstract

A proposal is made for the creation of macroscopic quantum states of collective atomic-ensemble variables by the use of stimulated Raman scattering (SRS), followed by conditional optical measurement. After the completion of the SRS process, one is able to reverse the process and to return all the atoms to their ground states in such a way that reads out an arbitrary quantum state of the collective atomic field and writes this state onto the outgoing optical field. This scheme can be used for the creation of entanglement between two distant atomic ensembles. The quantum analysis of the SRS process treats one-dimensional spatial-temporal propagation accurately. Remarkably, it is found that this multimode problem can be simplified to a two-mode problem involving spatial-temporal wave-packet modes of the optical and atomic collective fields. This improves the understanding of the entanglement created in this system.     

Vibration suppression of a CLD treated plate subject to a harmonic traveling load

Abstract

The vibrations of an annular plate with constrained layer damping (CLD) treatment subject to a traveling load are investigated. The equation of motion, after employing the assumed‐mode method, Donnell‐Mushtari‐Vlasov assumption and the Hamilton principle yielded terms of three plates’ displacements. The response is eventually, for each n, in terms of a single degree of freedom (SDOF) linear oscillator with hysteretic damping. The solution to a harmonic traveling load is then solved and discussed. Numerical results showed that the CLD treatment imposed significant damping onto the plate, especially as the plate reached its resonance. The interaction of harmonic driving frequency and traveling speed was also looked into. The results showed that to have the best damping effect, a relatively thin Visco Elastic Material (VEM) layer was enough and the damping was the most significant for n=0 and n=1 modes.     

Cavity optomechanics with a Bose–Einstein condensate: normal mode splitting

We study the normal mode splitting in a system consisting of a Bose–Einstein condensates (BECs) trapped inside a Fabry–Pérot cavity driven by a single mode laser field. We analyze the variations in frequency and damping rate of the collective density excitation of a BEC imparted by the optical field. We study the occurrence of normal mode splitting which appears as consequences of the hybridization of the fluctuations of the intracavity field and the condensate mode. It is shown that normal mode splitting vanishes for weak coupling between the condensate mode and the intracavity field. Moreover, we investigate the normal mode splitting in the transmission spectrum of the cavity field.     

The dynamics of three-mode coupling in a trapped Bose gas

ABSTRACT

Multiple mode couplings in topological coherent modes of Bose–Einstein condensate are considered, by introducing an external alternating (resonating) field in the system. This analysis is based on the analytical solutions of nonlinear Gross–Pitaevskii equation for a trapped Bose gas at nearly absolute zero temperature. The dynamics of fractional populations of the generated coherent modes are analysed, particularly for a three-level system in the limit of small to large detuning of the intermediate state. These coupled topological modes, though nonlinear, are analogous to a resonant atom and exhibit a variety of significant non-trivial phenomena (effects), like: dynamic phase transitions, interference patterns, critical phenomena, mode-locking and chaotic motion.     

Dispersion corrections to the collective mode spectrum in axial and planar phases of superfluid He3

Using the path integration technique developed by Brusov and Popov earlier, we have calculated for the first time the dispersion corrections to the collective mode spectrum in A- and 2D- phases of superfluidHe ³ for arbitrary directions of the collective excitation momentumk, taking the damping of collective modes into account. In axial-phase clapping (cl) mode remains six fold degenerate fork l, while for other directions a three fold splitting takes place, which reaches a maximum fork l. The pairbreaking modes remain degenerate even taking the dispersion induced corrections into account. In the planar phase the degeneracy of clapping (cl) and quasi-Goldstone (qGd) modes depends on the direction of the collective mode momentumk with respect to the external magnetic fieldH: the mode degeneracy remains the same as in the case of zero momentumk fork H only, and for any other directions two fold splitting of these modes takes place. The dispersion induced splitting of collective modes could be observed (at least in the A-phase) in sound absorption experiments.     

How to catch an atom with single photons

Abstract

We report on trapping a single neutral atom in the standing-wave light field of a high-finesse optical cavity containing one photon on average, a single-photon optical trap, or SPOT for short. This trap has the novel feature that the light field is also used to observe the atom in real time. The oscillatory motion of the trapped atom induces well-resolved oscillations of the light intensity. Periodic structure is visible in the fourth-order intensity correlation function, attributed to long-distance flights of the atom along the standing wave. The finite duration of those flights provides evidence for cavity-mediated cooling of atoms. We discuss the various mechanisms determining the trapping time and compare the results with a quantum-jump Monte Carlo simulation to interpret the observed signals.     

Vortex optical Magnus effect in multimode fibers

A theoretical and experimental analysis is made of the optical Magnus effect in multimode optical fibers excited by a laser beam whose wavefront has a pure screw dislocation and carries the topological charge ±l, where l is the azimuthal quantum number. It is found that the angular rotation of the plane of propagation of a local wave depends on the magnitude and sign of the topological charge and changes qualitatively when the circulation of the polarization is reversed. The phase mechanism is attributed to spin-orbit interaction in the photon ensemble. It is demonstrated experimentally that the optical Magnus effect in a few-mode fiber for the CP₁₁ mode at the beat length is observed as a rotation of the axis of the pure edge dislocation field through an angle proportional to the beat length. Pis’ma Zh. Tekh. Fiz. 23, 76–81 (August 26, 1997)     

Spatial Chaotic Power Cross-talk in Nonlinear Multibeam Co-propagation in Optical Fibres

Abstract

We investigate spatial power coupling and chaotic cross-talk when beams co-propagate in multimode optical fibres, specifically among four beams that belong to two weakly degenerate mode families. The nonlinear mechanism responsible for the power and phase coupling is the optical Kerr effect in fibres. The power of each of the modes is theoretically demonstrated to be spatially unstable and chaotically dependent on launch conditions. It is shown that the spatial instabilities and irregular energy exchange occur over broad operating conditions as long as the system deviates from its spatial steady states.     

Coherent Optical Phonon Oscillations in GaMnAs

Coherent phonon oscillations are investigated in a series of Ga_1–xMn_xAs layers with different Mn and hole concentrations. The longitudinal optical (LO)-phonon-hole-plasmon coupled mode oscillations are observed in layers with large Mn concentrations. The energies of these coupled modes depend on the hole concentrations, which may prove useful for determining this parameter in ferromagnetic alloys. Finally, electron-plasmon coupling with LO phonon, observed under optical excitation, is compared in GaMnAs and in LT-GaAs.