Using interaction-based readouts to approach the ultimate limit of detection noise robustness for quantum-enhanced metrology in collective spin systems

We consider the role of detection noise in quantum-enhanced metrology in collective spin systems, and derive a fundamental bound for the maximum obtainable sensitivity for a given level of added detection noise. We then present an interaction-based readout utilising the commonly used one-axis twisting scheme that approaches this bound for states generated via several commonly considered methods of generating quantum enhancement, such as one-axis twisting, two-axis counter-twisting, twist-and-turn squeezing, quantum non-demolition measurements, and adiabatically scanning through a quantum phase transition. We demonstrate that this method performs significantly better than other recently proposed interaction-based readouts. These results may help provide improved sensitivity for quantum sensing devices in the presence of unavoidable detection noise.

[1]  David E. Pritchard,et al.  Optics and interferometry with atoms and molecules , 2009 .

[2]  K. Mølmer,et al.  SPIN SQUEEZING IN AN ENSEMBLE OF ATOMS ILLUMINATED WITH SQUEEZED LIGHT , 1997 .

[3]  N. P. Bigelow,et al.  Atomic quantum non-demolition measurements and squeezing , 1998 .

[4]  R. J. Lewis-Swan,et al.  Quantum-Enhanced Sensing Based on Time Reversal of Nonlinear Dynamics. , 2016, Physical review letters.

[5]  G. Agarwal,et al.  Atomic Schrödinger cat states , 1997 .

[6]  Min Zhuang,et al.  Achieving Heisenberg-limited metrology with spin cat states via interaction-based readout , 2018, Physical Review A.

[7]  L. Pezzè,et al.  Spin-Mixing Interferometry with Bose-Einstein Condensates. , 2015, Physical review letters.

[8]  J I Cirac,et al.  Squeezing and entanglement of atomic beams. , 2000, Physical review letters.

[9]  R. J. Lewis-Swan,et al.  Robust Spin Squeezing via Photon-Mediated Interactions on an Optical Clock Transition. , 2018, Physical review letters.

[10]  C. Gerving,et al.  Spin-nematic squeezed vacuum in a quantum gas , 2011, Nature Physics.

[11]  Jelmer J. Renema,et al.  Entanglement-assisted atomic clock beyond the projection noise limit , 2009, 0912.3895.

[12]  N. J. Engelsen,et al.  Quantum phase magnification , 2016, Science.

[13]  L. Mandel,et al.  Generation of spin squeezing via continuous quantum nondemolition measurement , 2000, Physical review letters.

[14]  J. Schmiedmayer,et al.  Integrated Mach–Zehnder interferometer for Bose–Einstein condensates , 2013, Nature Communications.

[15]  Augusto Smerzi,et al.  Ultrasensitive two-mode interferometry with single-mode number squeezing. , 2013, Physical review letters.

[16]  S. Braunstein,et al.  Statistical distance and the geometry of quantum states. , 1994, Physical review letters.

[17]  Yun Li,et al.  Atom-chip-based generation of entanglement for quantum metrology , 2010, Nature.

[18]  Onur Hosten,et al.  Measurement noise 100 times lower than the quantum-projection limit using entangled atoms , 2016, Nature.

[19]  Matthias D. Lang,et al.  Heisenberg-limited metrology with information recycling , 2014, 1411.5111.

[20]  W. Ertmer,et al.  Improvement of an Atomic Clock using Squeezed Vacuum. , 2016, Physical review letters.

[21]  Coherent control of spin squeezing , 2000, quant-ph/0007056.

[22]  Samantha N. Hood,et al.  Squeezed-light-enhanced atom interferometry below the standard quantum limit , 2014, 1408.0067.

[23]  Outcoupling from a Bose-Einstein condensate with squeezed light to produce entangled-atom laser beams , 2005, quant-ph/0504069.

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

[25]  Quantum optics of a Bose-Einstein condensate coupled to a quantized light field , 1999, cond-mat/9902293.

[26]  S. Szigeti,et al.  Quantum metrology with mixed states: When recovering lost information is better than never losing it , 2015, 1507.03054.

[27]  Agarwal,et al.  Cooperative behavior of atoms irradiated by broadband squeezed light. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[28]  A. Sørensen,et al.  Quantum interface between light and atomic ensembles , 2008, 0807.3358.

[29]  L. Pezzè,et al.  Phase magnification by two-axis countertwisting for detection-noise robust interferometry , 2017, 1711.02658.

[30]  Firenze,et al.  Interferometric sensitivity and entanglement by scanning through quantum phase transitions in spinor Bose-Einstein condensates , 2017, 1712.03896.

[31]  L. Pezzè,et al.  Loschmidt Echo for quantum metrology , 2016, 1604.04246.

[32]  Augusto Smerzi,et al.  Fisher information and entanglement of non-Gaussian spin states , 2014, Science.

[33]  Min Zhuang,et al.  Non-Gaussian precision metrology via driving through quantum phase transitions , 2017, 1710.06290.

[34]  M. Schleier-Smith,et al.  Squeezing the collective spin of a dilute atomic ensemble by cavity feedback , 2009, 0911.3936.

[35]  D. Hume,et al.  Scalable spin squeezing for quantum-enhanced magnetometry with Bose-Einstein condensates. , 2014, Physical review letters.

[36]  Rafał Demkowicz-Dobrzański,et al.  The elusive Heisenberg limit in quantum-enhanced metrology , 2012, Nature Communications.

[37]  V. Vuletić,et al.  States of an ensemble of two-level atoms with reduced quantum uncertainty. , 2008, Physical review letters.

[38]  Holland,et al.  Interferometric detection of optical phase shifts at the Heisenberg limit. , 1993, Physical review letters.

[39]  Samuel P Nolan,et al.  Optimal and Robust Quantum Metrology Using Interaction-Based Readouts. , 2017, Physical review letters.

[40]  Augusto Smerzi,et al.  Not all pure entangled states are useful for sub-shot-noise interferometry , 2009, 0912.4349.

[41]  J. Kołodyński,et al.  Quantum limits in optical interferometry , 2014, 1405.7703.

[42]  V. Vuletić,et al.  Implementation of cavity squeezing of a collective atomic spin. , 2009, Physical review letters.

[43]  Self-induced spatial dynamics to enhance spin squeezing via one-axis twisting in a two component Bose-Einstein condensate , 2014, 1402.0307.

[44]  Klaus Mølmer,et al.  Entanglement and extreme spin squeezing. , 2000, Physical review letters.

[45]  W. Wootters.  Statistical distance and Hilbert space , 1981 .

[46]  Pavel Sekatski,et al.  Detecting Large Quantum Fisher Information with Finite Measurement Precision. , 2015, Physical review letters.

[47]  Gregory S. Bentsen,et al.  Approaching the Heisenberg Limit without Single-Particle Detection. , 2015, Physical review letters.

[48]  Philipp Treutlein,et al.  Quantum metrology with a scanning probe atom interferometer. , 2013, Physical review letters.

[49]  L. Duan,et al.  Generation of massive entanglement through an adiabatic quantum phase transition in a spinor condensate. , 2013, Physical review letters.

[50]  M. Oberthaler,et al.  Squeezing and entanglement in a Bose–Einstein condensate , 2008, Nature.

[51]  Quantum enhanced measurement of rotations with a spin-1 Bose-Einstein condensate in a ring trap , 2015, 1511.03364.

[52]  Jian Ma,et al.  Fisher information and spin squeezing in the Lipkin-Meshkov-Glick model , 2009, 0905.0245.

[53]  Meng Khoon Tey,et al.  QUANTUM ENTANGLEMENT: Deterministic entanglement generation from driving through quantum phase transitions , 2017 .

[54]  C. Adams,et al.  Contactless nonlinear optics mediated by long-range Rydberg interactions , 2017, Nature Physics.

[55]  R. J. Lewis-Swan,et al.  Pumped-Up SU(1,1) Interferometry. , 2016, Physical review letters.

[56]  M. Oberthaler,et al.  Nonlinear atom interferometer surpasses classical precision limit , 2010, Nature.

[57]  S. Haine.  Using interaction-based readouts to approach the ultimate limit of detection-noise robustness for quantum-enhanced metrology in collective spin systems , 2018, Physical Review A.

[58]  Ueda,et al.  Squeezed spin states. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[59]  W. Munro,et al.  Making the most of time in quantum metrology: concurrent state preparation and sensing , 2018, 1801.03452.

[60]  Samuel P. Nolan,et al.  Quantum Fisher information as a predictor of decoherence in the preparation of spin-cat states for quantum metrology , 2016, 1611.00533.

[61]  P. Meystre,et al.  Creating macroscopic atomic Einstein-Podolsky-Rosen states from Bose-Einstein condensates. , 2000, Physical review letters.

[62]  Samuel P. Nolan,et al.  Robustifying twist-and-turn entanglement with interaction-based readout , 2018, 1803.08789.

[63]  J. M. Radcliffe.  Some properties of coherent spin states , 1971 .

[64]  S. Lloyd,et al.  Quantum metrology. , 2005, Physical review letters.

[65]  W. Ertmer,et al.  Twin Matter Waves for Interferometry Beyond the Classical Limit , 2011, Science.

[66]  G. Tóth,et al.  Multipartite entanglement and high precision metrology , 2010, 1006.4368.

[67]  Chaohong Lee.  Adiabatic Mach-Zehnder interferometry on a quantized Bose-Josephson junction. , 2006, Physical review letters.

[68]  Augusto Smerzi,et al.  Fisher information and multiparticle entanglement , 2010, 1006.4366.