LINEAR QUANTUM TRAJECTORIES : APPLICATIONS TO CONTINUOUS PROJECTION MEASUREMENTS

We present a method for obtaining evolution operators for linear quantum trajectories. We apply this to a number of physical examples of varying mathematical complexity, in which the quantum trajectories describe the continuous projection measurement of physical observables. Using this method we calculate the average conditional uncertainty for the measured observables, being a central quantity of interest in these measurement processes.

[1]  P. Knight,et al.  The Quantum jump approach to dissipative dynamics in quantum optics , 1997, quant-ph/9702007.

[2]  Vitali,et al.  Effect of feedback on the decoherence of a Schrödinger-cat state: A quantum trajectory description. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[3]  W. Strunz Linear quantum state diffusion for non-Markovian open quantum systems , 1996, quant-ph/9610035.

[4]  Strunz Stochastic path integrals and open quantum systems. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[5]  Wiseman,et al.  Adaptive phase measurements of optical modes: Going beyond the marginal Q distribution. , 1995, Physical review letters.

[6]  Steinbach,et al.  High-order unraveling of master equations for dissipative evolution. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[7]  Graham,et al.  Schrödinger cat states and single runs for the damped harmonic oscillator. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[8]  Milburn,et al.  Quantum-limited measurements with the atomic force microscope. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[9]  Graham,et al.  Linear stochastic wave equations for continuously measured quantum systems. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[10]  Milburn,et al.  Squeezing via feedback. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[11]  N. Gisin,et al.  Explicit examples of dissipative systems in the quantum state diffusion model , 1993 .

[12]  Milburn,et al.  Continuous position measurements and the quantum Zeno effect. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[13]  Milburn,et al.  Interpretation of quantum jump and diffusion processes illustrated on the Bloch sphere. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[14]  H. Carmichael An open systems approach to quantum optics , 1993 .

[15]  Milburn,et al.  Quantum theory of field-quadrature measurements. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[16]  Gardiner,et al.  Monte Carlo simulation of master equations in quantum optics for vacuum, thermal, and squeezed reservoirs. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[17]  Ueda,et al.  Continuous quantum-nondemolition measurement of photon number. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[18]  D. Chruściński,et al.  On the asymptotic solutions of Belavkin's stochastic wave equation , 1992 .

[19]  K. Mølmer,et al.  Wave-function approach to dissipative processes in quantum optics. , 1992, Physical review letters.

[20]  V. Belavkin,et al.  Nondemolition observation of a free quantum particle. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[21]  V. Belavkin,et al.  Measurements continuous in time and a posteriori states in quantum mechanics , 1991, Journal of Physics A: Mathematical and General.

[22]  Phase squeezing using intracavity subharmonic generation , 1991 .

[23]  Ueda Nonequilibrium open-system theory for continuous photodetection processes: A probability-density-functional description. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[24]  Ozawa Quantum-mechanical models of position measurements. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[25]  Masahito Ueda,et al.  Probability-density-functional description of quantum photodetection processes , 1989 .

[26]  V. Belavkin,et al.  A quantum particle undergoing continuous observation , 1989, quant-ph/0512137.

[27]  N. Gisin Stochastic quantum dynamics and relativity , 1989 .

[28]  Milburn,et al.  Quantum-mechanical model for continuous position measurements. , 1987, Physical review. A, General physics.

[29]  Problems of quantum theory of continuous measurements , 1986 .

[30]  Diósi Comments on continuous observation in quantum mechanics. , 1986, Physical Review D, Particles and fields.

[31]  Pérès,et al.  Quantum measurements of finite duration. , 1985, Physical review. D, Particles and fields.

[32]  N. Gisin Quantum measurements and stochastic processes , 1984 .

[33]  The quantum measurement process and the observation of continuous trajectories , 1984 .

[34]  Generalized stochastic processes and continual observations in quantum mechanics , 1983 .

[35]  C. Gardiner Handbook of Stochastic Methods , 1983 .

[36]  Alberto Barchielli,et al.  A model for the macroscopic description and continual observations in quantum mechanics , 1982 .

[37]  M. D. Srinivas,et al.  Photon Counting Probabilities in Quantum Optics , 1981 .

[38]  V. Sandberg,et al.  ON THE MEASUREMENT OF A WEAK CLASSICAL FORCE COUPLED TO A QUANTUM MECHANICAL OSCILLATOR. I. ISSUES OF PRINCIPLE , 1980 .

[39]  Oluwole Adetunji,et al.  Remarks on the Wilson-Zimmermann expansion and some properties of them-point distribution , 1976 .

[40]  G. Lindblad On the generators of quantum dynamical semigroups , 1976 .

[41]  Wolfgang Witschel,et al.  Ordered operator expansions by comparison , 1975 .

[42]  G. Agarwal Quantum statistical theories of spontaneous emission and their relation to other approaches , 1974 .

[43]  W. Louisell Quantum Statistical Properties of Radiation , 1973 .

[44]  H. F. Baker,et al.  Alternants and Continuous Groups , 1905 .