Continuous quantum measurement process in stochastic phase-methods of quantum dynamics: Classicality from quantum measurement

Transcription

1 Continuous quantum measurement process in stochastic phase-methods of quantum dynamics: Classicality from quantum measurement Janne Ruostekoski University of Southampton Juha Javanainen University of Connecticut

2 Outline Classical vs quantum in continuous measurement process BEC in a double-well system Monitor atom number by light scattering Incorporate back-action of measurement in a classical stochastic description Measurement-induced back-action drives the system to classical behaviour

3 Stochastic (approximate) representation of quantum systems Wigner phase-space methods for nonlinear dynamics Synthesize stochastic representation for initial state of quantum field that generates QM correlation functions Effect of thermal and quantum fluctuations unravelled into stochastic trajectories that obey classical mean-field dynamics QM expectation values and uncertainties from ensemble averages Gross, Esteve, Oberthaler, Martin, Ruostekoski, PRA 84, (2011) reduced onsite fluctuations long-range correlations in weakly coupled BECs spin-squeezing

4 Double-well system Time evolution after unbalanced initial state

5 Continuous quantum measurement Continuous monitoring of atom numbers by off-resonant light scattering (photon counting) Ruostekoski, Walls, PRA 58, R50 (1998)

6 Quantum dynamics Nonlinear dynamics & quantum measurement-induced back-action from detection of spontaneously scattered photons Solve using stochastic state vectors: Quantum trajectory simulations Dalibard, Castin, Molmer, PRL 68, 580 (1992) Dum Zoller, Ritsch, PRA 45, 4879 (1992) Tian, Carmichael, PRA 46, R6801 (1992) Quantum jumps in a trajectory a faithful simulation of photon counting events in a single experimental run

7 Stochastic phase-space description Replace operators by complex numbers Wigner function Gardiner, Zoller, Quantum Noise Walls, Milburn, Quantum Optics Equation of motion:

8 canonical pairs Poisson brackets Transformation Canonical transformation total atom number relative atom number absolute phase relative phase Liouville with Hamiltonian

9 Total atom number Introduce: Approximate model Keep constant expand t W (z,ϕ,t) = mean field theory + Γ 2 ϕ 2 W (z,ϕ,t) Measurement back-action described by phase diffusion W is always a valid classical probability distribution

10 Stochastic dynamics Langevin equation Unravel density matrix evolution into stochastic realizations Each individual realization represents possible outcome of single experimental run Sample stochastically quantum fluctuations in the initial state Truncated Wigner method for open system with quantum measurement-induced back-action

11 Initial state Initially tilted double-well potential fl Initial population imbalance Include quadratic fluctuations of atoms fl quantum statistical description of atoms (squeezed state) Wigner function classical stochastic distribution Remove energy imbalance fl atom number oscillations

12 Individual trajectories Outcome of single experimental run (classical & quantum) classical full quantum Approximately 10 detected photons per oscillation

13 Ensemble averages N=100 quantum classical no measurement continuous measurement Without measurements results differ Measurements drive system towards classical dynamics

14 Extreme quantum N=10 quantum classical no measurement continuous measurement Valid in very small atom number limit

15 Classical vs quantum Emergent classicality in quantum limit due to measurement-induced back-action More generic phenomenon of indistinguishability of continuously observed systems? Quantum measurement-driven Schrödinger cat states in many-particle systems Ruostekoski et al., PRA 57, 511 (1998)

16 Concluding remarks Essential ingredient: Back-action of measurement Classical stochastic phase-space description of measurement within truncated Wigner method Classicality driven by continuous measurement