Beyond Heisenberg uncertainty principle in the negative mass reference frame. Eugene Polzik Niels Bohr Institute Copenhagen

Transcription

1 Beyond Heisenberg uncertainty principle in the negative mass reference frame Eugene Polzik Niels Bohr Institute Copenhagen

2 Trajectories without quantum uncertainties with a negative mass reference frame Towards spin mechanical oscillator entanglement Ω L Ĵ

3 Position X and momentum P noncommuting variables P Xˆ, Pˆ = i X Var * * < ( X ) Var( P ) 1/ 4

4 Klemens Hammerer See also: Tsai and Caves, PRL 2010 M. Ozawa Special issue "Quantum and Hybrid Mechanical Systems From Fundamentals to Applications" of Annalen der Physik 527, No. 1 2, A15 A20 (2015). W. Wasilewski et al. Phys. Rev. Lett., 104, (2010). K. Hammerer et al. Phys. Rev. Lett. 102, (2009).

5 3 steps to noiseless quantum trajectories 1. Trajectory is defined relative to a quantum origin 2. The origin system has an effective negative mass 3. Entangled state of the origin system and the system of interest is generated Trajectories without quantum uncertainties. K. Hammerer and ESP, Special issue "Quantum and Hybrid Mechanical Systems From Fundamentals to Applications" of Annalen der Physik. (2015) arxiv: Establishing Einstein-Podolsky-Rosen channels between nanomechanics and atomic ensembles. K. Hammerer, M. Aspelmeyer, ESP, P. Zoller. PRL 102, (2009).

6 Trajectory with respect to a quantum origin P+P 0 P+P 0 X-X 0 X-X 0 Entangled (EPR) state relative to origin EPR state relative to a negative mass origin Y Y0 Y Y0 X X0 X X0

7 Negative and positive mass oscillators Oscillator in classical coordinate frame: Xˆ, Pˆ = i Oscillator in quantum reference frame with respect to a negative mass (m = - m 0 = 1) reference oscillator: Entanglement condition Var ( X 0 X 0 ) + Var( P + P ) < 2

8 Beam splitter, entangling and QND Hamiltonians in optomechanics Memory Entanglement QND H= χ abˆ + abˆ+ hc Par ˆ χ ˆ BS.. ω SiN membrane Yeghishe Tsaturyan photon phonon

9 Spin ensemble at K = ground state harmonic oscillator [ J ˆ ] z, J ˆ y = ij x J N = i= 1 j i Harmonic oscillator in the ground state at room temperature. Spin noise = projection noise of I0> J z ~X Xˆ, Pˆ = i 1/2-1/2 J x J y ~P Negative frequency oscillator S. L. Christensen et al. PRA Vuletic group, Nature 2015 ˆ ˆ ˆ ˆ ˆ J X P i X b b P bˆ = = + = = b = 1 z i A, A A ( ), ( ) 2 A 2 Jx Xˆ Pˆ Jˆ y J x

10 Room temperature atom trap with 10 msec coherence time Spin T 2 = 10 msec µ 10 8 Cesium spins Microcell coated with 1-octadecene and 1- nonadecene.

11 Harmonic ocsillator a 1/2 b Bi-linear coupling of photons to collective spin oscillator ˆ χ ˆ BS.. -1/2 H= χ abˆ + abˆ+ hc 2 χpˆ Pˆ, if χ = χ Par Quantum NonDemolition input-output relations photon Measurement Back action Atomic spin L A Par BS

12 Entanglement of an oscillator with an effective negative mass leads to back action evading measurement beyond SQL Synchronized to better than Standard Quantum Limit Ĵ Positive frequency oscillator J y J z Var( X ) + Var( P + ) < J Negative frequency oscillator m F = 2 J ˆb 1 m F = 3 2 m F = 4 Zeeman splitting

13 Cartoon: Quantum noise components and Back Action cancellation Vacuum noise Ĵ z Spin quantum Membrane drive R<<1 Spin Phase Reference LO R<<1 Spin Membrane back action Membrane quantum Spin drive Spin back action Membrane drive Spin back action π/2 phase shift Spin back action Lock-in amplifier Back action : Stark shift due to quantum noise in polarization ellipticity Back action : radiation pressure due to quantum amplitude fluctuations

14 Albert Schliesser Christoffer Møller Rodrigo Thomas and Giorgos Vasilakis

15 Observation of the opposite back action signs for both X and P for a mechanical oscillator and a spin oscillator (negative mass) EOM Spin oscillator at Larmor frequency Mechanical oscillator at (1,1) mode Backaction in X ~ cos Ω t Backaction in P ~ sin Ω t August 18, 2015

16 10 4 photons per BW K Membrane Spin. Positive mass Spin. Negative mass Joint X quadrature 610 khz 20 khz m F = - 4 m F = -3 m F = 3 m F = 4 Y quadrature

17 Time synchronization beyond SQL with negative mass reference frame arxiv:

18 Squeezed state of an oscillator by stroboscopic Quantum Nondemolition Measurement Ĵ Nature Physics 11, (2015)

19 Squeezed state of an oscillator by stroboscopic Quantum Nondemolition Measurement RF magnetic field E Ĵ y z S ˆ () t 2 Cavity finesse 15 m F = 4 a 3 6P 3/ 2 b 6S 1/ 2 2 H = χa bˆ + abˆ + h c Cavity enhanced interaction ˆ χˆ.. Nature Physics 11, (2015)

20 Primer: Back action evading stroboscopic measurement on an oscillator X Ĵ Y Z Continuous measurement leads to growing backaction Stroboscopic measurement at 2Ω is backaction free Y X Y X Z Z Ground state projection noise Nature Physics 11, (2015) Original proposal Braginsky et al, 1970s

21 Squeezed state of an oscillator Ĵ Nature Physics 11, (2015)

22 CV photonic interface with 1D atomic crystal Juergen Appel Joerg Helge Muller Guided probe 0.05 absorption/atom Jean-Baptiste Beguin Heidi Sorensen 2000 atoms Single pass cooperativity = optical depth ~ 10 Theory collaboration: Ivan Iakoupov Anders Sorensen Rauschenbeutel, Kimble, Laurat, Hakuta, Nic Cormaic, Orozco

23 Collective reflection from trapped atoms Trapped atoms at 1056/2nm distance but probe is 852nm Burn a new structure with 852nm standing wave

24 Reflection from a 400 atom string 35% Amplitude reflection Reflection from disordered atoms

25 y z Detector Ĵ Inverted reference oscillator Lock-in amplifier

26 An object can have a noiseless trajectory only in one coordinate system Entanglement monogamy Y Y0 X X0 All coordinate systems are equal, but some are more equal than others George Orwell. Animal Farm

27 Temperature versus mode temperature Mode noise temperature 1/2-1/2 Xˆ -1/2 1/2 Pˆ Negative mass oscillator

28 Negative relative noise temperature Entangled state of two oscillators P Mechanical Oscillator P Initial thermal state Ground state X X Magnetic Oscillator Experiment: Time without a jump at 8K Relative temperature < 0 K