IMPROVED QUANTUM MAGNETOMETRY

Transcription

1 (to appear in Physical Review X) IMPROVED QUANTUM MAGNETOMETRY BEYOND THE STANDARD QUANTUM LIMIT Janek Kołodyński ICFO - Institute of Photonic Sciences, Castelldefels (Barcelona), Spain Faculty of Physics, University of Warsaw, Poland joined work with: Jonatan Bohr Brask Department of Theoretical Physics, University of Geneva, Switzerland Rafael Chaves Institute for Physics, University of Freiburg, Germany Institute for Theoretical Physics, University of Cologne, Germany

2 OVERVIEW QUANTUM METROLOGY: SUPER-CLASSICAL RESOLUTIONS OF MEASUREMENTS Precision beyond classical statistics, theoretically reaching the Heisenberg Limit (HL):. Experiments beyond the Standard Quantum Limit (SQL) with optical interferometry, atomic spectroscopy, atomic magnetometry QUANTUM METROLOGY WITH UNCORRELATED NOISE Local noise severely constraints the precision: Proposals of fighting the decoherence effects: non-markovian (with memory) dynamics, error-correction methods, transversal noise: IMPROVED QUANTUM MAGNETOMETRY EXPERIMENT OF WASILEWSKI ET AL. Real-life implementation of the transversal dephasing-noise model with its validity analysed. For the experimental parameters of PRL 104, (2010) improvement of precision due to modification of the geometry employed can reach even 3 orders of magnitude (N = ).

3 QUANTUM METROLOGY IN OPTICAL INTERFEROMETRY MACH-ZEHNDER INTERFEROMETER (specially no hats!!) Jordan-Schwinger representation: Error-propagation formula (narrow fluctuations of around its mean): Input-output relations: Coherent state strategy: shot noise (SQL) Coherent-squeezed vacuum strategy: not! quite HL [R. Demkowicz-Dobrzański, M. Jarzyna, J. Kołodyński Quantum limits in optical interferometry, Progress in Optics 60, 345 (2015), arxiv: ]

4 QUANTUM METROLOGY IN ATOMIC SPECTROSCOPY RAMSEY INTERFEROMETER Total angular momentum representation: Error-propagation formula: is the parameter of interest and total time for experiment,, is also a resource! also optimisation of t!!! Coherent-spin state: One-axis-twisted spin-squeezed state (OATSS): shot noise (SQL) not! quite HL [R. Demkowicz-Dobrzański, M. Jarzyna, J. Kołodyński Quantum limits in optical interferometry, Progress in Optics 60, 345 (2015), arxiv: ]

5 NOISY QUANTUM METROLOGY IN ATOMIC SPECTROSCOPY RAMSEY INTERFEROMETER WITH UNCORRELATED DEPHASING Single atom: N atoms: Error-propagation formula: One-axis-twisted spin-squeezed state (OATSS): Back to SQL!! [D. Ulam-Orgikh and M. Kitagawa, Phys. Rev. A 64, (2001)]

6 NOISY QUANTUM METROLOGY BEYOND SQL? Abstract theoretical idea of transversal dephasing: Single atom: N atoms: Motivation preserve decoherence-free regime up to second-order O(t 2 ) at short time scales, as in Quantum Zeno Effect. By use of precision-bounding methods of J. Kołodyński & R. Demkowicz-Dobrzański [New Journal of Physics (2013)] we were able to show that maximally entangled GHZ states: optimally achieve for But is it just a mathematical peculiarity, or may such a geometry phenomenon be utilised to counterbalance decoherence in a real-life, physical impementation?

7 RECONSIDERATION OF THE MAGNETOMETRY EXPERIMENT OF W. WASILEWSKI ET AL [PRL 104, (2010)] B = 0.92 G = 92 μt B rf = 36 ft Ω B =2κB= 3 MHz T 2 << T 1 Relevant noise source: (local) spin decoherence T 2. Ignore: (local) spin relaxation T 1. (global) ensemble spin decoherence and relaxation (T 2*, T 1 * ). Moving to the Rotating Frame (RF) dictated by: Single atom: N atoms:, we have: Exactly the dynamics of transversal dephasing!!! But how do the OATSS perform, i.e., how to prepare the atoms and which J-component to measure? with Scenario (a) as in PRL 104, (2010): Atoms prepared along the B-field. Squeezed in y-direction. Measurement of J y in RF (details) is performed. Scenario (b) superior!!!!: Atoms prepared transversally to both B and B rf. Squeezed in x-direction. Measurement of J x in RF is performed.

8 Scenario (a) : SUMMARY OF RESULTS IN OATSS-BASED STRATEGY Scenario (b) : SQL exactly as if the noise was parallel!! Not optimal (1/N 5/6 ), yet still significantly enhanced. Optimally setting single-shot duration, t(n), and squeezing parameter μ(n)!!! Improvement over coherent-spin states assuming experimental parameters of Wasilewski et al: (a) (Fixed t, just optimizing squeezing strength μ(n).) Scenario (a) : Ideally: At (max) -8dB: Scenario (b) : Ideally: At (max) -8dB: (b) (a) (b)

9 SUMMARY OF RESULTS IN OATSS-BASED STRATEGY (OTHER NOISE SOURCES) General master equation (effectively spin-relaxation-like depolarisation noise): and in the Rotating Frame (RF): Scenarios: Model-robustness to other sources of decoherence (spin relaxation T 1 ): (a) (b)

10 CONCLUSIONS AND ISSUES Single-shot time, t, optimisation lower limit set by the apparatus,. Other sources of decoherence, in particular, spin relaxation ( ). Establish optimal regimes in which their effects can be minimised. Measurement implementation originally two cells employed. Can we really move easily to the Rotating Frame (RF) preserving full control? Implementation of spin-squeezing originally two-axis-twisted spin-squeezed (TATSS) states prepared via QND and light-atom interactions. But these should, however, perform only better!!! Dependence of the results on the estimated magnetic field. Potential adaptive strategies (with Bayesian techniques. ) analysed with use of We really need to study what can be done in a real experiment! 8 vs 2x10 7 Thank You For Your Attention