Mach-Zehnder interferometry at the Heisenberg limit with coherent and squeezed-vacuum light.

We show that the phase sensitivity Deltatheta of a Mach-Zehnder interferometer illuminated by a coherent state in one input port and a squeezed-vacuum state in the other port is (i) independent of the true value of the phase shift and (ii) can reach the Heisenberg limit Deltatheta approximately 1/N(T), where N(T) is the average number of input particles. We also demonstrate that the Cramer-Rao lower bound of phase sensitivity, Deltatheta approximately 1/square root[|alpha|(2)e(2r)+sinh(2)r], can be saturated for arbitrary values of the squeezing parameter r and the amplitude of the coherent mode alpha by using a Bayesian phase inference protocol.

[1]  Lane,et al.  Maximum-likelihood statistics of multiple quantum phase measurements. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[2]  D Bouwmeester,et al.  Quantum entanglement of a large number of photons. , 2004, Physical review letters.

[3]  Jeffrey H. Shapiro,et al.  Squeezed states in phase-sensing interferometers , 1984 .

[4]  Kirk McKenzie,et al.  Experimental demonstration of a squeezing-enhanced power-recycled michelson interferometer for gravitational wave detection. , 2002, Physical review letters.

[5]  Augusto Smerzi,et al.  Phase sensitivity of a Mach-Zehnder interferometer , 2006 .

[6]  Hall,et al.  Generation of squeezed states by parametric down conversion. , 1986, Physical review letters.

[7]  Karsten Danzmann,et al.  Demonstration of a squeezed-light-enhanced power- and signal-recycled Michelson interferometer. , 2005, Physical review letters.

[8]  A. Luis,et al.  Mode Transformation Properties and Quantum Limits for a Fabry-Perot Interferometer , 1991 .

[9]  Braunstein.  Quantum limits on precision measurements of phase. , 1992, Physical review letters.

[10]  Jonathan P. Dowling,et al.  A quantum Rosetta stone for interferometry , 2002, quant-ph/0202133.

[11]  Andrey B. Matsko,et al.  Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and/or output optics , 2001 .

[12]  M. S. Zubairy,et al.  Quantum optics: Frontmatter , 1997 .

[13]  Wiseman,et al.  Optimal states and almost optimal adaptive measurements for quantum interferometry , 2000, Physical review letters.

[14]  B. Yurke,et al.  Squeezed-light-enhanced polarization interferometer. , 1987, Physical review letters.

[15]  D. Walls.  Squeezed states of light , 1983, Nature.

[16]  John K. Stockton,et al.  Adaptive homodyne measurement of optical phase. , 2002, Physical review letters.

[17]  Kimble,et al.  Precision measurement beyond the shot-noise limit. , 1987, Physical review letters.

[18]  S. Schiller,et al.  Measurement of the quantum states of squeezed light , 1997, Nature.

[19]  Karsten Danzmann,et al.  Coherent control of vacuum squeezing in the gravitational-wave detection band. , 2006, Physical review letters.

[20]  A Smerzi,et al.  Phase detection at the quantum limit with multiphoton Mach-Zehnder interferometry. , 2007, Physical review letters.

[21]  C. Fabre,et al.  Ultimate quantum limits for resolution of beam displacements , 2003 .

[22]  C. Caves.  Quantum Mechanical Noise in an Interferometer , 1981 .

[23]  R. B. Blakestad,et al.  Creation of a six-atom ‘Schrödinger cat’ state , 2005, Nature.

[24]  H. Briegel,et al.  Experimental demonstration of five-photon entanglement and open-destination teleportation , 2004, Nature.

[25]  S. Lloyd,et al.  Quantum-Enhanced Measurements: Beating the Standard Quantum Limit , 2004, Science.

[26]  Matteo G. A. Paris,et al.  Small amount of squeezing in high-sensitive realistic interferometry , 1995 .

[27]  Hidehiro Yonezawa,et al.  Observation of -9 dB quadrature squeezing with improvement of phase stability in homodyne measurement. , 2007, Optics express.

[28]  R. Loudon.  Quantum Limit on the Michelson Interferometer used for Gravitational-Wave Detection , 1981 .

[29]  Gerd Leuchs,et al.  Squeezed States for Interferometric Gravitational-wave Detectors , 1987 .

[30]  Wineland,et al.  Optimal frequency measurements with maximally correlated states. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[31]  H. Yuen.  Two-photon coherent states of the radiation field , 1976 .

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

[33]  Klauder,et al.  SU(2) and SU(1,1) interferometers. , 1986, Physical review. A, General physics.

[34]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.