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Page 1: Introduction into Quantum Optomechanics

Introduction into QuantumOptomechanics

Part 2 of 2

F.Ya.Khalili

March 20, 2013

1 / 70

Page 2: Introduction into Quantum Optomechanics

1 Standard Quantum Limit

2 Quantum speedmeter

3 Negative optical inertia

4 Some metaphysics

5 Non-gaussian optomechanics

2 / 70

Page 3: Introduction into Quantum Optomechanics

1 Standard Quantum Limit

2 Quantum speedmeter

3 Negative optical inertia

4 Some metaphysics

5 Non-gaussian optomechanics

3 / 70

Page 4: Introduction into Quantum Optomechanics

LENGTHY EQUATIONS AHEAD!

4 / 70

Page 5: Introduction into Quantum Optomechanics

Detection of classical force

Freemass

x(t)

F fl(t)

Meter“x(t)” = x(t) + xfl(t)F sign(t)

5 / 70

Page 6: Introduction into Quantum Optomechanics

Detection of classical force

Freemass

x(t)

F fl(t)

Meter“x(t)” = x(t) + xfl(t)F sign(t)

−mΩ2x(Ω) = F sign(Ω) + F fl(Ω)

“x(Ω)” = x(Ω) + xfl(Ω) =F sign(Ω)

−mΩ2+

the sum noise︷ ︸︸ ︷F fl(Ω)

−mΩ2+ xfl(Ω)

6 / 70

Page 7: Introduction into Quantum Optomechanics

Detection of classical force

Freemass

x(t)

F fl(t)

Meter“x(t)” = x(t) + xfl(t)F sign(t)

−mΩ2x(Ω) = F sign(Ω) + F fl(Ω)

“x(Ω)” = x(Ω) + xfl(Ω) =F sign(Ω)

−mΩ2+

the sum noise︷ ︸︸ ︷F fl(Ω)

−mΩ2+ xfl(Ω)

Ssum(Ω) = Sx +2SxF−mΩ2

+SF

m2Ω4

=~2/4 + S2

xF

SF+

2SxF−mΩ2

+SF

m2Ω4

7 / 70

Page 8: Introduction into Quantum Optomechanics

Detection of classical force

Freemass

x(t)

F fl(t)

Meter“x(t)” = x(t) + xfl(t)F sign(t)

Ssum(Ω) = Sx +2SxF−mΩ2

+SF

m2Ω4

=~2/4 + S2

xF

SF+

2SxF−mΩ2

+SF

m2Ω4

Classical optimization: damn the back action!

8 / 70

Page 9: Introduction into Quantum Optomechanics

Detection of classical force

Freemass

x(t)

F fl(t)

Meter“x(t)” = x(t) + xfl(t)F sign(t)

Ssum(Ω) = Sx +2SxF−mΩ2

+SF

m2Ω4

=~2/4 + S2

xF

SF+

2SxF−mΩ2

+SF

m2Ω4

Classical optimization: damn the back action!

SxF = 0 ⇒ Ssum(Ω) = Sx +SF

m2Ω4=

~2m

(1

Ω2q

+Ω2

q

Ω4

)

Ωq =

(SF

m2Sx

)1/4

∝√〈I 〉m

e2r

9 / 70

Page 10: Introduction into Quantum Optomechanics

Sum noise spectral densityS

(Ω)

Ω

Sx

SFm2Ω4

Ssum(Ω) =~

2m

(1

Ω2q

+Ω2

q

Ω4

)

Ω = Ωq

10 / 70

Page 11: Introduction into Quantum Optomechanics

Sum noise spectral densityS

(Ω)

Ω

Ω (1)q

<

Ω (2)q

<

Ω (3)q

<

Ω (4)q

<

Ω (5)q

11 / 70

Page 12: Introduction into Quantum Optomechanics

Standard Quantum LimitS

(Ω)

Ω

SSQL (Ω) = ~

mΩ 2

12 / 70

Page 13: Introduction into Quantum Optomechanics

Standard Quantum LimitS

(Ω)

Ω

“Quantum”

“Classical”

SSQL (Ω) = ~

mΩ 2

m = 40 kg , Ω = 2π × 100 s−1 ⇒√SSQL ≈ 2.5× 10−21 m/

√Hz

13 / 70

Page 14: Introduction into Quantum Optomechanics

Standard Quantum LimitS

(Ω)

Ω

“Quantum”

“Classical”

SSQL (Ω) = ~

mΩ 2

m = 40 kg , Ω = 2π × 100 s−1 ⇒√SSQL ≈ 2.5× 10−21 m/

√Hz

14 / 70

Page 15: Introduction into Quantum Optomechanics

How to overcome the SQL

Implicit assumptions that have been made:

1 The scheme is stationary (invariant with respect totime shift).

2 The noises are Markovian.

3 The noise are mutually uncorrelated.

4 The test object is a free mass.

Number of schemes based on violation of some of theseassumptions has been proposed.

Only one successful experiment was performed / (fornow).

15 / 70

Page 16: Introduction into Quantum Optomechanics

How to overcome the SQL

Implicit assumptions that have been made:

1 The scheme is stationary (invariant with respect totime shift).

2 The noises are Markovian.

3 The noise are mutually uncorrelated.

4 The test object is a free mass.

Number of schemes based on violation of some of theseassumptions has been proposed.

Only one successful experiment was performed / (fornow).

16 / 70

Page 17: Introduction into Quantum Optomechanics

Questions?

17 / 70

Page 18: Introduction into Quantum Optomechanics

1 Standard Quantum Limit

2 Quantum speedmeter

3 Negative optical inertia

4 Some metaphysics

5 Non-gaussian optomechanics

18 / 70

Page 19: Introduction into Quantum Optomechanics

SQL: simplified consideration

Position measurement

x(t) = x +pt

m+

1

m

∫ t

0

(t − t ′)F (t ′) dt ′

[x(0), x(t)] =i~tm⇒ ∆x(0) = ∆x(t) >

√~t2m

Ssum >(∆x)2

Ω∼ ~

mΩ2

Momentum measurement

p(t) = p(0) +

∫ t

0

F (t ′) dt ′ ⇒ [p(0), p(t)] = 0

⇒ no SQL

Velocity measurement

We can not measure momentum?Let us measure velocity instead!

19 / 70

Page 20: Introduction into Quantum Optomechanics

SQL: simplified consideration

Position measurement

x(t) = x +pt

m+

1

m

∫ t

0

(t − t ′)F (t ′) dt ′

[x(0), x(t)] =i~tm⇒ ∆x(0) = ∆x(t) >

√~t2m

Ssum >(∆x)2

Ω∼ ~

mΩ2

Momentum measurement

p(t) = p(0) +

∫ t

0

F (t ′) dt ′ ⇒ [p(0), p(t)] = 0

⇒ no SQL

Velocity measurement

We can not measure momentum?Let us measure velocity instead!

20 / 70

Page 21: Introduction into Quantum Optomechanics

SQL: simplified consideration

Position measurement

x(t) = x +pt

m+

1

m

∫ t

0

(t − t ′)F (t ′) dt ′

[x(0), x(t)] =i~tm⇒ ∆x(0) = ∆x(t) >

√~t2m

Ssum >(∆x)2

Ω∼ ~

mΩ2

Momentum measurement

p(t) = p(0) +

∫ t

0

F (t ′) dt ′ ⇒ [p(0), p(t)] = 0

⇒ no SQL

Velocity measurement

We can not measure momentum?Let us measure velocity instead!

21 / 70

Page 22: Introduction into Quantum Optomechanics

The idea

Light interacts with the probe twice:

V.B.Braginsky, F.Ya.Khalili, Phys.Lett.A 147, 251 (1990)22 / 70

Page 23: Introduction into Quantum Optomechanics

The idea

Light interacts with the probe twice:

V.B.Braginsky, F.Ya.Khalili, Phys.Lett.A 147, 251 (1990)23 / 70

Page 24: Introduction into Quantum Optomechanics

Sagnac interferometerDelay lines

aRN

bRN

bLN

aLN

aRE

bRE

aLE

bLEBS

SRM

PRM

z

Laser

p q

PD

ITM ETM

ITM

ETM

Ring cavities

aRN bRN

bLN

aLN

aRE

bRE

aLE

bLE

BS

SRM

PRM

ETM

ETM

z

Laser

p q

PD

Yanbei Chen, Phys.Rev.D 67, 122004 (2003)

24 / 70

Page 25: Introduction into Quantum Optomechanics

Sagnac interferometerDelay lines

aRN

bRN

bLN

aLN

aRE

bRE

aLE

bLEBS

SRM

PRM

z

Laser

p q

PD

ITM ETM

ITM

ETM

Ring cavities

aRN bRN

bLN

aLN

aRE

bRE

aLE

bLE

BS

SRM

PRM

ETM

ETM

z

Laser

p q

PD

δφ(t) ∝ xnorth(t − τ) + xeast(t)

δφ(t) ∝ xeast(t − τ) + xnorth(t)

δφ(t)− δφ(t) ∝ τd

dt[xeast(t)− xnorth(t)]

25 / 70

Page 26: Introduction into Quantum Optomechanics

Overview of 1m speed meter experiment

!  1g mirrors suspended in monolithic fused silica suspensions.

!  1kW of circulating power. Arm cavities with finesse of 10000. 100ppm loss per roundtrip.

!  Sophisticated seismic isolation + double pendulums with one vertical stage.

!  Large beams to reduce coating noise.

!  Armlength = 1m. Target better than 10-18m/sqrt(Hz) at 1kHz.

!  No recycling, no squeezing, but plan to use homodyne detection.

!  LOTS OF CHALLENGES! (let me know if you want to help…)

S.Hild et al, LSC QNWG telecon, January 30, 201326 / 70

Page 27: Introduction into Quantum Optomechanics

Questions?

27 / 70

Page 28: Introduction into Quantum Optomechanics

1 Standard Quantum Limit

2 Quantum speedmeter

3 Negative optical inertia

4 Some metaphysics

5 Non-gaussian optomechanics

28 / 70

Page 29: Introduction into Quantum Optomechanics

The idea

SSQL =~

mΩ2

It is assumed that minert = mgrav = m. But what if not?

29 / 70

Page 30: Introduction into Quantum Optomechanics

The idea

SSQL =~

mΩ2

It is assumed that minert = mgrav = m. But what if not?

SSQL(Ω) =~minert

m2gravΩ4

30 / 70

Page 31: Introduction into Quantum Optomechanics

The idea

SSQL =~

mΩ2

It is assumed that minert = mgrav = m. But what if not?

SSQL(Ω) =~minert

m2gravΩ4

minert

mgrav→ 0 ⇒ SSQL(Ω)→ 0

31 / 70

Page 32: Introduction into Quantum Optomechanics

The idea

SSQL =~

mΩ2

It is assumed that minert = mgrav = m. But what if not?

SSQL(Ω) =~minert

m2gravΩ4

minert

mgrav→ 0 ⇒ SSQL(Ω)→ 0

Impossible? But...

F.Khalili et al, Phys. Rev. D 83, 062003 (2011)

32 / 70

Page 33: Introduction into Quantum Optomechanics

Optical springs to help

Mechanical responce function:

χ−1(Ω) = −mΩ2 + K

33 / 70

Page 34: Introduction into Quantum Optomechanics

Optical springs to help

Mechanical responce function:

χ−1(Ω) = −mΩ2 + K

Two optical springs (γ δ, just for simplicity):

K ≈ 4ωp〈I1〉cL

δ1

δ21 − Ω2

+4ωp〈I2〉cL

δ2

δ22 − Ω2

34 / 70

Page 35: Introduction into Quantum Optomechanics

Optical springs to help

Mechanical responce function:

χ−1(Ω) = −mΩ2 + K

Two optical springs (γ δ, just for simplicity):

K ≈ 4ωp〈I1〉cL

δ1

δ21 − Ω2

+4ωp〈I2〉cL

δ2

δ22 − Ω2

〈I 〉1δ1

+〈I 〉2δ2

= 0 , Ω δ1,2 ⇒ K ≈ −µΩ2

µ =4ωp

cL

〈I1〉δ1 + 〈I2〉δ2

δ21 + δ2

2

: the optical inertia!

35 / 70

Page 36: Introduction into Quantum Optomechanics

Optical springs to help

Mechanical responce function:

χ−1(Ω) = −mΩ2 + K

Two optical springs (γ δ, just for simplicity):

K ≈ 4ωp〈I1〉cL

δ1

δ21 − Ω2

+4ωp〈I2〉cL

δ2

δ22 − Ω2

〈I 〉1δ1

+〈I 〉2δ2

= 0 , Ω δ1,2 ⇒ K ≈ −µΩ2

µ =4ωp

cL

〈I1〉δ1 + 〈I2〉δ2

δ21 + δ2

2

: the optical inertia!

mgrav = m , minert = m + µ

µ < 0 ⇒ minert < mgrav36 / 70

Page 37: Introduction into Quantum Optomechanics

Questions?

37 / 70

Page 38: Introduction into Quantum Optomechanics

1 Standard Quantum Limit

2 Quantum speedmeter

3 Negative optical inertia

4 Some metaphysics

5 Non-gaussian optomechanics

38 / 70

Page 39: Introduction into Quantum Optomechanics

~F = m~a

(deterministic!)

Quantum-classical cut

i~d |ψ〉dt

= H |ψ〉

(deterministic!)

39 / 70

Page 40: Introduction into Quantum Optomechanics

~F = m~a (deterministic!)

Quantum-classical cut

i~d |ψ〉dt

= H |ψ〉

(deterministic!)

40 / 70

Page 41: Introduction into Quantum Optomechanics

~F = m~a (deterministic!)

Quantum-classical cut

i~d |ψ〉dt

= H |ψ〉 (deterministic!)

41 / 70

Page 42: Introduction into Quantum Optomechanics

~F = m~a (deterministic!)

Quantum reduction: THE randomness!

i~d |ψ〉dt

= H |ψ〉 (deterministic!)

42 / 70

Page 43: Introduction into Quantum Optomechanics

The root of all evil:the (in)famous Reduction Postulate:

|ψn〉 =En|ψ〉√

Pn

Pn = 〈ψ|En|ψ〉

which cuts off randomly brunchesof the World Wave Function.

43 / 70

Page 44: Introduction into Quantum Optomechanics

Where and when the reduction REALLY happens?

• Copenhagen interpretation: We do not know and donot want to know; shut up and calculate theprobabilities.

• David Bohm: Reduction is a human invention. Thereal world is classical (but non local!)

• Eugene Wigner: Reduction happens in the humanbrain (which does not obey the ordinary laws ofphysics)

• Hugh Everett: Reduction is a human invention. Thereal world is completely quantum.

• Most of the physicists (in their subconsciousness):Reduction happens somewhere in meso-scale (andtherefore open systems blah blah blah...)

44 / 70

Page 45: Introduction into Quantum Optomechanics

Where and when the reduction REALLY happens?

• Copenhagen interpretation: We do not know and donot want to know; shut up and calculate theprobabilities.

• David Bohm: Reduction is a human invention. Thereal world is classical (but non local!)

• Eugene Wigner: Reduction happens in the humanbrain (which does not obey the ordinary laws ofphysics)

• Hugh Everett: Reduction is a human invention. Thereal world is completely quantum.

• Most of the physicists (in their subconsciousness):Reduction happens somewhere in meso-scale (andtherefore open systems blah blah blah...)

45 / 70

Page 46: Introduction into Quantum Optomechanics

Where and when the reduction REALLY happens?

• Copenhagen interpretation: We do not know and donot want to know; shut up and calculate theprobabilities.

• David Bohm: Reduction is a human invention. Thereal world is classical (but non local!)

• Eugene Wigner: Reduction happens in the humanbrain (which does not obey the ordinary laws ofphysics)

• Hugh Everett: Reduction is a human invention. Thereal world is completely quantum.

• Most of the physicists (in their subconsciousness):Reduction happens somewhere in meso-scale (andtherefore open systems blah blah blah...)

46 / 70

Page 47: Introduction into Quantum Optomechanics

Where and when the reduction REALLY happens?

• Copenhagen interpretation: We do not know and donot want to know; shut up and calculate theprobabilities.

• David Bohm: Reduction is a human invention. Thereal world is classical (but non local!)

• Eugene Wigner: Reduction happens in the humanbrain (which does not obey the ordinary laws ofphysics)

• Hugh Everett: Reduction is a human invention. Thereal world is completely quantum.

• Most of the physicists (in their subconsciousness):Reduction happens somewhere in meso-scale (andtherefore open systems blah blah blah...)

But what about cats?47 / 70

Page 48: Introduction into Quantum Optomechanics

Where and when the reduction REALLY happens?

• Copenhagen interpretation: We do not know and donot want to know; shut up and calculate theprobabilities.

• David Bohm: Reduction is a human invention. Thereal world is classical (but non local!)

• Eugene Wigner: Reduction happens in the humanbrain (which does not obey the ordinary laws ofphysics)

• Hugh Everett: Reduction is a human invention. Thereal world is completely quantum.

• Most of the physicists (in their subconsciousness):Reduction happens somewhere in meso-scale (andtherefore open systems blah blah blah...)

48 / 70

Page 49: Introduction into Quantum Optomechanics

Where and when the reduction REALLY happens?

• Copenhagen interpretation: We do not know and donot want to know; shut up and calculate theprobabilities.

• David Bohm: Reduction is a human invention. Thereal world is classical (but non local!)

• Eugene Wigner: Reduction happens in the humanbrain (which does not obey the ordinary laws ofphysics)

• Hugh Everett: Reduction is a human invention. Thereal world is completely quantum.

• Most of the physicists (in their subconsciousness):Reduction happens somewhere in meso-scale (andtherefore open systems blah blah blah...)

49 / 70

Page 50: Introduction into Quantum Optomechanics

The most consistent options

• Copenhagen interpretation: We do not know and donot want to know; shut up and calculate theprobabilities.

• David Bohm: Reduction is a human invention.The real world is classical (but non local!)

• Eugene Wigner: Reduction happens in the humanbrain (which does not obey the ordinary law ofphysics)

• Hugh Everett: Reduction is a human invention.The real world is completely quantum.

• Most of the physicists (in their subconsciousness):Reduction happens somewhere in meso-scale(and therefore open systems blah blah blah...)

50 / 70

Page 51: Introduction into Quantum Optomechanics

The options which can be tested

• Copenhagen interpretation: We do not know and donot want to know; shut up and calculate theprobabilities.

• David Bohm: Reduction is a human invention.The real world is classical (but non local!)

• Eugene Wigner: Reduction happens in the humanbrain (which does not obey the ordinary law ofphysics)

• Hugh Everett: Reduction is a human invention.The real world is completely quantum.

• Most of the physicists (in their subconsciousness):Reduction happens somewhere in meso-scale(and therefore open systems blah blah blah...)

51 / 70

Page 52: Introduction into Quantum Optomechanics

The paper to read tonight

Lev Vaidman, “On schizophrenic experiences of theneutron or why we should believe in the many-worldsinterpretation of quantum theory”,arXiv:quant-ph/9609006

52 / 70

Page 53: Introduction into Quantum Optomechanics

The Gaussianity problem

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

0.2

0.4

0.6

0.8

1.0

Quantum Wignerfunction W (x , p) of

|ψ〉 = |0〉.

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

0.2

0.4

0.6

0.8

1.0

Classical probabilitydistribution W (x , p) for

T =~Ω0

2kB

Find any difference!

53 / 70

Page 54: Introduction into Quantum Optomechanics

The Gaussianity problem

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

0.2

0.4

0.6

0.8

1.0

Quantum Wignerfunction W (x , p) of

|ψ〉 = |0〉.

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

0.2

0.4

0.6

0.8

1.0

Classical probabilitydistribution W (x , p) for

T =~Ω0

2kBFind any difference!

54 / 70

Page 55: Introduction into Quantum Optomechanics

An always positive Wigner function can serve as thehidden-variable probability distribution with respect tomeasurements corresponding to any linear combinationof x and p.

J. S. Bell, Speakable and Unspeakable in Quantum Mechanics,Cambridge Univ. Press, Cambridge, 1987

S. L. Braunstein, P. van Loock, RMP 77, 513 (2005)

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

−1.0

−0.8

−0.6

−0.4

−0.2

0.0

0.2

0.4

The real tests ofquantumness requirenon-linear measurementsor non-Gaussian states.

55 / 70

Page 56: Introduction into Quantum Optomechanics

An always positive Wigner function can serve as thehidden-variable probability distribution with respect tomeasurements corresponding to any linear combinationof x and p.

J. S. Bell, Speakable and Unspeakable in Quantum Mechanics,Cambridge Univ. Press, Cambridge, 1987

S. L. Braunstein, P. van Loock, RMP 77, 513 (2005)

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

−1.0

−0.8

−0.6

−0.4

−0.2

0.0

0.2

0.4

The real tests ofquantumness requirenon-linear measurementsor non-Gaussian states.

56 / 70

Page 57: Introduction into Quantum Optomechanics

1 Standard Quantum Limit

2 Quantum speedmeter

3 Negative optical inertia

4 Some metaphysics

5 Non-gaussian optomechanics

57 / 70

Page 58: Introduction into Quantum Optomechanics

Generic scheme of experiment

• Prepare some really macroscopic mechanical objectin a really non-classical (non-Gaussian) state.

• Show that this state can survive for considerabletime (no spontaneous reduction!)

• Unprepare the mechanical object back to its initialstate (crucial for Everett’s point of view)

It would be good to include into the last step also theguy who do this experiment (resolving thus the Wigner’sfriend paradox).

58 / 70

Page 59: Introduction into Quantum Optomechanics

Generic scheme of experiment

• Prepare some really macroscopic mechanical objectin a really non-classical (non-Gaussian) state.

• Show that this state can survive for considerabletime (no spontaneous reduction!)

• Unprepare the mechanical object back to its initialstate (crucial for Everett’s point of view)

It would be good to include into the last step also theguy who do this experiment (resolving thus the Wigner’sfriend paradox).

59 / 70

Page 60: Introduction into Quantum Optomechanics

Generic scheme of experiment

• Prepare some really macroscopic mechanical objectin a really non-classical (non-Gaussian) state.

• Show that this state can survive for considerabletime (no spontaneous reduction!)

• Unprepare the mechanical object back to its initialstate (crucial for Everett’s point of view)

It would be good to include into the last step also theguy who do this experiment (resolving thus the Wigner’sfriend paradox).

60 / 70

Page 61: Introduction into Quantum Optomechanics

Generic scheme of experiment

• Prepare some really macroscopic mechanical objectin a really non-classical (non-Gaussian) state.

• Show that this state can survive for considerabletime (no spontaneous reduction!)

• Unprepare the mechanical object back to its initialstate (crucial for Everett’s point of view)

It would be good to include into the last step also theguy who do this experiment (resolving thus the Wigner’sfriend paradox).

61 / 70

Page 62: Introduction into Quantum Optomechanics

Mechanical non-Gaussian preparation

Two ways:

• Direct use the mechanical non-linearity.

Impossible at the current technological level (?):mechanical systems are too linear and too noisy.

• Injection of an optical non-Gaussian state into themechanical resonator.

The way to go?

62 / 70

Page 63: Introduction into Quantum Optomechanics

Mechanical non-Gaussian preparation

Two ways:

• Direct use the mechanical non-linearity.Impossible at the current technological level (?):mechanical systems are too linear and too noisy.

• Injection of an optical non-Gaussian state into themechanical resonator. The way to go?

63 / 70

Page 64: Introduction into Quantum Optomechanics

Direct linear interaction: simple and effective

Ωmech ωe.m.

Λ

Hint = −~K (a + a†)x

Ωmech = ωe.m.

|φ〉|ψ〉 ⇐⇒t=π/Λ

|ψ〉|φ〉

(feasible in microwave band)64 / 70

Page 65: Introduction into Quantum Optomechanics

Up-converting: effective as well

Ωmech ωe.m.− ωp

Λ

Hint = −2~G (Ae−iωpt a + A∗e iωpt a†)x

ωp = ωe.m. − Ωmech

|φ〉|ψ〉 ⇐⇒t=π/Λ

|ψ〉|φ〉

(feasible in both microwave and optical bands)65 / 70

Page 66: Introduction into Quantum Optomechanics

The idea

The setup is identical tothe optical cooling in theresolved sideband regime.

The only difference:the input field ina non-Gaussian state,instead of the ground one.

J.Zhang, K.Peng, and S.L.Braunstein, PRA 68, 013808 (2003)

66 / 70

Page 67: Introduction into Quantum Optomechanics

The idea

The setup is identical tothe optical cooling in theresolved sideband regime.

The only difference:the input field ina non-Gaussian state,instead of the ground one.

J.Zhang, K.Peng, and S.L.Braunstein, PRA 68, 013808 (2003)

67 / 70

Page 68: Introduction into Quantum Optomechanics

(A bit) more real-world proposal

Adaption to LIGO and table-top interferometers.

F.Khalili et al, PRL 105, 070403 (2010)68 / 70

Page 69: Introduction into Quantum Optomechanics

Quantum memory?

Storage times of:

optical cavities: . 10−3 s

MW resonators: . 1 s

mechanical pendulums: up to 108 s!

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Page 70: Introduction into Quantum Optomechanics

Shrodinger cat in AdvLIGO?

M = 40 kg70 / 70