Optomechanicswith Blue Detuning - cQOM · Macroscopic Quantum Mechanics: Theory and Experimental Concepts of Optomechanics Y. Chen J Phys. B 46 104001 (2013) Quantum Optomechanics-throwing

Optomechanics with Blue Detuning

Klemens Hammerer

Centre for Quantum Engineeringand Space-Time Research

Leibniz University HannoverInstitute for Theoretical Physics

Institute for Gravitational Physics (AEI)

Summer School on Optomechanics – Les Houches – Aug 2015

2

Optomechanics in 1920s

3

Gedankenexperiment #1: Heisenberg microscope

Heisenberg, The Physical Principles of the Quantum Theory, 1930

uncertainty in Compton recoil

4

Standard Quantum Limit in Position Sensing

free mass

measure position to precision

momentum has uncertainty

uncertainty in position at later time

amplitude

phase

measurement back action

observed in cavity optomechanical system: Purdy et al, Science 339, 801 (2013)

5

Gedankenexperiment #2: Optical Cooling of Mirror & its Quantum Limits

“On the development of our conception regarding the nature and constitution of radiation.”

Talk at “81st meeting of the Society of Natural Scientists and Medics” Salzburg 1909

6

Doppler shift of reflected wave

force due to momentum transfer on mirror

Radiation provides friction


for power

7

Doppler shift of reflected wave

force due to momentum transfer on mirror

Radiation provides friction

limitation is given by (quantum) fluctuations of EM field subject to Plancks law


for power

temperature

Doppler cooling

observed in cavity optomechanical system (with resolved sideband cooling):Chan Nature 478, 89 (2011), Teufel, Nature 475, 359 (2011).

8

Quantum effects so far in optomechanics (incl. μw electromechanics)

» ground state cooling

» Quantum coherent coupling

» ponderomotive squeezing

» back action noise in position sensing

» quantum coherent state transfer

» optomechanical entanglement

» feedback control within decoherence time

» Quantum squeezing of motion

Chan Nature 478, 89 (2011).Teufel, Nature 475, 359 (2011).

Safavi-Naeini, Nature 500, 185 (2013).Brooks, Nature 488, 476 (2012).

Purdy, Science 339, 801 (2013).

O’Connell, Nature 464, 697 (2010)Palomaki, Nature 495, 210 (2013)

Palomaki, Science 342, 710 (2013)

Roukes, Schwab (2005)

KH, Science 342 702 (2013)

Verhagen, Nature 482, 63 (2012).

Wilson, arXiv:1410.6191 (2014)

Wollman, arXiv:1507,01662 (2015)

9

Optomechanical systems

radiation pressure interaction


LIGO – Laser Interferometer Gravitational Wave Observatory

D. Bowmeester, Santa Barbara/Leiden

up to

Mechanical SystemsCoupled to Light

Quantum OptomechanicsM. Aspelmeyer, F. Marquardt, T. Kippenberg,RMP, arXiv:1303.0733

Macroscopic Quantum Mechanics: Theory and Experimental Conceptsof OptomechanicsY. ChenJ Phys. B 46 104001 (2013)

Quantum Optomechanics - throwing a glanceM. Aspelmeyer, S. Groeblacher, KH, N. KieselJOSA B 27, A189 (2010)

12


radiation pressure interaction

for

M. Aspelmeyer, F. Marquardt, T. Kippenberg, RMP, arXiv:1303.0733

example:

13

effective coupling strength

number of circulating photons


for

linearized radiation pressure interaction

for 1mW and 1 MHz line width

strong coupling & normal mode splitting

14

Optomechanical Cooperativity

condition for quantum coherent dynamics:

large optomechanical cooperativity

15

Quantum effects so far in optomechanics (incl. μw electromechanics)

» ground state cooling

» Quantum coherent coupling

» ponderomotive squeezing

» back action noise in position sensing

» quantum coherent state transfer

» optomechanical entanglement

» feedback control within decoherence time

» Quantum squeezing of motion

Quantum Effects in Optomechanics

Chan Nature 478, 89 (2011).Teufel, Nature 475, 359 (2011).

Safavi-Naeini, Nature 500, 185 (2013).Brooks, Nature 488, 476 (2012).

Purdy, Science 339, 801 (2013).

O’Connell, Nature 464, 697 (2010)Palomaki, Nature 495, 210 (2013)

Palomaki, Science 342, 710 (2013)

Verhagen, Nature 482, 63 (2012).

Wilson, arXiv:1410.6191 (2014)

Wollman, arXiv:1507,01662 (2015)

16

Optomechanical “Phase Diagramm”

C. Genes, D. Vitali et al. Phys. Rev. A 77, 033804 (2008)

-2 -1 0 1 20.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

unstable

unstable

stable

couplingstrength

detuning

cooperativity

1

2

5

10

17

Resonant Drive: Position Sensing

-2 -1 0 1 20.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

couplingstrength

detuning

cooperativity

1

2

5

10

measurement back action: Purdy, Science 339, 801 (2013).

“QuantumNon-Demolitioninteraction”

18

Red Detuned Drive: Optomechanical Cooling

-2 -1 0 1 20.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

couplingstrength

detuning

cooperativity

1

2

5

10

ground state cooling

Chan Nature 478, 89 (2011)Teufel, Nature 475, 359 (2011)

19

Blue Detuned Drive

-2 -1 0 1 20.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

couplingstrength

detuning

cooperativity

1

2

5

10

?

20

Resonant interaction is entangling

Compare to parametric down-conversion in nonlinear optics:

Blue detuned drive: Optomechanical Heating

pump

Ou, Pereira, Kimble, Peng,PRL 68, 3663 (1992)

opticalmode

opticalmode

opticalmode

21

Digression: Two Mode Squeezing

Squeezed states of two modes

each mode looks like it was in a thermal state

overall state is pure with corresponding wave function

22

Digression: EPR Correlations

for infinite squeezing this corresponds to the ideal EPR state

Center of mass position and relative momentum take sharp values

for two mode squeezed states with finite squeezing limit for uncorrelated states in ground state

23

Digression: Entanglement

Two mode squeezed states are entangled: cannot be written as product state

a mixed states is entangled if it can not be written as a mixture of product states

general EPR entanglement criterion for two modes

for Gaussian states this is necessary & sufficient (slightly generalized)

a state is entangled if

limit for uncorrelated states in ground state

Duan PRL (2000)Simon PRL (2000)

24

Drive on upper sideband creates entanglement

Problem: System is dynamically unstable for blue detuned drive

use a pulsed drive: solve scattering problem

Blue detuned drive unstable regime

Sebastian G. Hofer, Witlef Wieczorek, Markus Aspelmeyer, KHPhys. Rev. A 84, 052327 (2011) O. Romero-Isart et al., Physical Review A 83, 013803 (2011)

noise

optically induced damping and frequency shifty

25

Pulsed Generation of Entanglement

integrate for pulse suration

central frequency at upper sideband

assuming

weak thermal decoherence

sideband resolved limit for suppression of Anti-Stokes scattering

weak coupling: adiabatic elimination of cavity mode (avoid memory effects)

Sebastian G. Hofer, Witlef Wieczorek, Markus Aspelmeyer, KHPhys. Rev. A 84, 052327 (2011)

26

will generate photons at cavity frequency in precise temporal mode

input-output relations for scattered pulse

squeezing parameter


two mode squeezed state!

mode profile

27


EPR variance, taking into account initial thermal occupation of mirror

if

large EPR squeezing requires large cooperativity:

for pulse length

squeezing parameter

for


28

drive system on first red sideband:

mechanical state is swapped to light

entanglement preparation and verification:

measure EPR quadratures of 1st and 2nd pulse and correlate

Verification of entanglement

Palomaki, Nature 495, 210 (2013)

time

Precoolingon red sideband

entangling pulseon blue sideband

readout pulseon red sideband

entanglement

red out

1st pulse

2nd pulse

mec


29

mw optomechanical system:

Experiment by Lehnert group

Entangling mechanical motion with microwave fieldsT. A. Palomaki, J. D. Teufel, R. W. Simmonds, and K. W. Lehnert

Science 342 6159 (2013)

news & views:KH, Science 342 6159 (2013)

Einstein-Podolsky-Rosen variance:

30

Optomechanical Entanglement

Two-mode squeezed (Gaussian), entangled state of a macroscopic (micron-sized) mechanical oscillator and a travelling pulse of (mw) light

31

quantum effects so far…

– demonstrate large cooperativity

– rely on linear dynamics

– use homodyne detections

– preserve Gaussian states

– therefore, have an equivalent classical interpretation (with some level of noise)

Quantum Optomechanics

32

Galland, Sangouard, Piro, Gisin, Kippenberg, PRL 112, 143602 (2014)



detection of single photon projects mechanical oscillator in single phonon Fock state

33

Photon-Counting in Electro-Mechanics

qubit cavity

Lecocq, arXiv: 1409.0872

qubittransition

frequency

photonnumberin cavity

34


qubit cavity


qubittransition

frequency


0 1 2 3 4

35


qubit cavity


qubittransition

frequency


+ measurement of qubit in e0 1 2 3 4

36

Galland, Sangouard, Piro, Gisin, Kippenberg, PRL 112, 143602 (2014)



detection of single photon projects mechanical oscillator in single phonon Fock state

37

Bell Inequality for Binary Observables

source of entangled systems A & B

CHSH Inequality (implied by realism & locality)

For two (effective) spin ½ systems in singlet state:

rules out (realism and locality)

38

Add coherent amplitude before detection

define the binary observable

Binary Observable for Bosonic Modes

no click

click!no click

Banaszek, PRL 82, 2009 (1999)

39

Bell Inequality in Optomechanics

0) Initialization of mechanics in ground state by red sideband cooling

1) Optomechanical entanglement by blue sideband pulse

2) Displacement by amplitude α & photon counting

3) Swap of mechanical state to photons by red sideband pulse

4) Displacement by amplitude β & photon counting

Repeat for various measurement setting α and β and infer

S.G. Hofer, K.W. Lehnert, KH, arXiv:1506.08097V. Caprara Vivoli, T. Barnea, C. Galland, N. Sangouard, arXiv:1506.06116

40

Realization in Electro-Mechanics

qubit cavity


optomechanical master equation for cascaded cavity setup:

S.G. Hofer, K.W. Lehnert, KH, arXiv:1506.08097

41

Bell Inequality in Optomechanics

cooperativity

Bellviolation

transmittivity

For parameters of: T. A. Palomaki, Science 342 6159 (2013) with solid (dashed)

Includes thermal decoherence, finite detection efficiency, transmission lossesS.G. Hofer, K.W. Lehnert, KH, arXiv:1506.08097

42

Beyond pulsed entanglement: Continuous Drive on Blue Sideband

• Nonlinear quantum equations of motion

• consider corresponding nonlinear classical nonlinear dynamics

+ noise

+ noise

Experiment:Anetsberger, Nat. Phys. (2009)

Theory:Marquardt, Ludwig, see RMP, arXiv:1303.0733

43

Limit Cycles

• Classical equations of motion

• slowly varying amplitude

solution

intensity

Marquardt, Ludwig…RMP, arXiv:1303.0733

off resonant terms

44

Limit Cycles

• mechanical amplitude

• nonlinear optical damping

classical:Marquardt, Ludwig…RMP, arXiv:1303.0733

quantum:J. Qian, A. Clerk, KH, F. Marquardt, PRL 109, 253601 (2012)N. Lörch, J. Qian, A. Clerk, F. Marquardt, KH, arXiv:1310.1298, PRX (2014)

45

Quantum Theory of Limit Cycles

• Radiation pressure Hamiltonian is nonlinear

For sufficiently strong coupling per single photon g0 the dynamics will be Non-Gaussian.

• Do Non-Gaussian features persist in steady state? Negative Wigner Functions?

Master Equation

thermal contact

cavity decaydriving field

46

Quantum Mechanical Steady State

• Solve master equation for steady state

for (rather extreme) parameters

• Wigner function

detuning

Qian, Clerk, KH, MarquardtPRL 109, 253601, 2012

A

47




• Wigner function

detuning


B

48




• Wigner function

detuning

C


49




• Wigner function

detuning


D

50


• Wigner functions

• Phonon number and Fano factorNegativeWigner

functions

co

olin

gh

eatin

g


51

Laser theory approach provides Fokker-Planck equation for mechanical oscillator

Can exhibit sub-Poissonian phonon statistics & negative Wigner functions

Limit Cycles in the Quantum Regime

Oscillation amplitude r

dam

pin

gdiff

usio

n

J. Qian, A. Clerk, KH, F. Marquardt, PRL 109, 253601 (2012)N. Lörch, J. Qian, A. Clerk, F. Marquardt, KH, PRX 4, 011015 (2014)

52



53

Use for Quantum Teleportation

feedback

VB Aentangled

Bell measurementfeedback

Bennett PRL 1993

continuous variables:Braunstein, Kimble PRL 2003

Vaidman PRL 2003


54

Time Continuous Bell Measurements & Teleportation

continuous wave drive on upper sideband, continuous Bell measurement & (stabilizing) feedback?

55

“time continuous quantum remote control”

Time Continuous Teleportation in Optomechanics

cooperativity

6dB inputsqueezing

Gaussian input

mechanical squeezing:• parametric drive• reservoir engineering• QND probeVitali, Clerk, MarquardtBraginsky, Aspelmeyer,Schwab, Nunnenlamp…

Hofer, Vasilyev, Aspelmeyer, KH, PRL 111, 170404 (2013)Hofer, KH PRA 91, 033822 (2015)

56

Time Continuous Entanglement Swapping in Optomechanics

EPR squeezinglog negativity

generates deteriministic, stationary entanglement

Hofer, Vasilyev, Aspelmeyer, KH, PRL 111, 170404 (2013)Hofer, KH PRA 91, 033822 (2015)

cooperativity

57


EPR squeezinglog negativity

generates deteriministic, stationary entanglement tolerant to losses and finite detection efficiency

transmissivity

Hofer, Vasilyev, Aspelmeyer, KH, PRL 111, 170404 (2013)Hofer, KH arXiv:1411.1337

cooperativity

58


10 m prototype @ AEI

Michelson interferometer!

in context of GWD setups:Y. Chen, PRL 100 013601 (2008)

Hofer, Vasilyev, Aspelmeyer, KH, PRL 111, 170404 (2013)Hofer, KH arXiv:1411.1337

59

Summary

-2 -1 0 1 20.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

couplingstrength

detuning

cooperativity

1

2

5

10

coolingstate swap

position sensingforce sensing

measurement back action

heatingentanglementFock state preparationBell testsquantum control via measurement & feedbacknonclassical limit cycle states

former members:

Niels Loerch (Basel)

Sergey Tarabrin

Andre Xuereb (Malta)

Albert EinsteinInstitute

Institute forTheoretical Physics

Centre for Quantum Engineering and Space-

Time Research

Group:

Sebastian Hofer

Ondrej Cernotik

Alexander Roth

Jonas Lammers

Marius Schulte

Hashem Zoubi

Klemens Hammerer

Thank you!

Support through:DFG (QUEST, GRK 1991)EC (MALICIA, iQUOEMS)Vienna (WWTF)

optomechanical transducerCollaborators on optomechanics

Konrad Lehnert (JILA)Philipp Treutlein (Basel)Peter Zoller (Innsbruck)Eugene Polzik (Copenhagen)Florian Marquardt (Erlangen)Ash Clerk (McGill)Roman Schnabel (Hamburg)Farit Khalili (Moscow)Markus Aspelmeyer (Vienna)Klaus Hornberger (Duisburg)

Documents

Optomechanicswith Blue Detuning - cQOM · Macroscopic Quantum Mechanics: Theory and Experimental Concepts of Optomechanics Y. Chen J Phys. B 46 104001 (2013) Quantum Optomechanics-throwing