Quantum Correlations of Light Mediated by Gravity Haixing Miao - - PowerPoint PPT Presentation

Quantum Correlations of Light Mediated by Gravity

Haixing Miao

MaQS Workshop @ Imperial College London

Institute of Gravitational Wave Astronomy

University of Birmingham

• H. Miao, D. Martynov, and H. Yang, Quantum Correlations of Light Mediated by Gravity, arXiv: 1901.05827

Quantum effect of gravity

x1 x2

+ +

One classical gravity model Classical spacetime Quantum matter

Entanglement Gµν = 8πG c4 hψ| ˆ Tµν|ψi

1

• Interaction between two objects

Single object but in a superposition Neither producing superposed spacetime nor creating bipartite quantum entanglement

• C. Møller, Colloques Internationaux CNRS 91, 1 (1962).
• L. Rosenfeld, Nuclear Physics 40, 353 (1963).

2 [1] S. Bose, A. Mazumdar, G. Moley, H. Ulbricht, M. Toros, M. Paternostro, A. Geraci, P. Barker, M. Kim, and G. Milburn, Spin Entanglement Witness for Quantum Gravity, Phys. Rev. Lett. 119, 240401 (2017). [2] C. Marletto, and V. Vedral, Gravitationally Induced Entanglement between Two Massive Particles is Sufficient Evidence of Quantum Effects in Gravity, Phys. Rev. Lett. 119, 240402 (2017).

Using two matter-wave interferometers:

• [1] Y. Chen, MQM: theory and experimental concepts of optomechanics, J. Phys. B: AMO Phys. 46 104001 (2013).

[2] M. Aspelmeyer et al., Cavity optomechanics, Rev. Mod. Phys. 86, 1391 (2014).

From nano-gram to kilogram

Caltech & NIST UCSB` LIGO MIT Vienna Yale JILA AEI LKB Laser Optical cavity Mechanical oscillator (mirror)

Optomechanics

Mechanics modulates the optical phase; Radiation pressure affects the mechanics.

EPFL 3

• Optomechanical

cooperativity: Laser Optical cavity Mechanical oscillator (mirror)

Optomechanics

Mechanics modulates the optical phase; Radiation pressure affects the mechanics.

4

Characteristic parameters: C ∝ PcavFQm m

¯ nth = kBT ~ωm

Thermal

• ccupation number:

Quantum radiation pressure dominated regime [1-3]: C ≥ ¯ nth

[1] T. Purdy, R. Peterson, and C. Regal, Science 339, 801 (2013). [2] C. B. Møller, R. A. Thomas, G. Vasilakis et al., Nature 547, 191 (2017). [3] M. Rossi, D. Mason, J. Chen, Y. Tsaturyan, and A. Schliesser, Nature 563, 53 (2018).

5

Using two optomechanical devices

Characteristic frequency:

(typically 0.1 mHz)

A B

( ˆ QA,B ≡ ˆ xA,B p 2mωm/~)

ˆ HAB = Gm2 |d + ˆ xA − ˆ xB| ≈ Gm2 d + ~ ω2

g

ωm ˆ QA ˆ QB

Gravitational interaction rate is low

ωg = p Λ G ρ

6

Gaussian bipartite entanglement:

VA

VAB

V0

AB

VB

XA

XB

YA

YB

XA

XB

YA

YB

Covariance Matrix:

Turns out to be equally applicable to non-Gaussian matter-wave interferometers.

[1] R. Simon, Phys. Rev. Lett. 84, 2726 (2000). [2] R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009). [3] S. Qvarfort, S. Bose, and A. Serafini, arXiv: 1812.09776 (2018).

Applying Simon’s entanglement criterion [1, 2, 3] leads to

γmkBT ≤ ~ ω2

g

VAB =  0 G∗ G

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|G| = 2 p CACB Qm ✓ ωg ωm ◆2

(only determined by mechanical property!)

7

Applying to the proposed scheme: In terms of temperature to quality factor ratio:

T Qm ≤ 1.5 × 10−18K ✓ Λ 2.0 ◆ ✓ 1 Hz ωm/2π ◆ ✓ ρ 19 g/cm3 ◆

A B

This is beyond the state-of-the-art of optomechanics.

γmkBT ≤ ~ ω2

g

(γm = ωm/Qm , ω2

g = ΛGρ)

8

VA

VAB

V0

AB

VB

XA

XB

YA

YB

XA

XB

YA

YB

VAB =  0 G∗ G

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|G| = 2 p CACB Qm ✓ ωg ωm ◆2

A B

Amplitude fluctuation of A Quantum radiation pressure Test mass A Test mass B Phase fluctuation of B Gravitational interaction Phase modulation

Signal-to-Noise Ratio SNR ∝ τ 1/2

int

✓ CA ¯ nB

th

◆1/2

increases as the integration time

Cross-correlation Measurement:

9 A B

Cross-correlation Measurement:

τint ≈ 1.0 year ✓ ¯ nth/C 0.4 ◆ ✓ωm/2π 1 Hz ◆3 ✓ 106 Qm ◆ ✓19 g/cm3 ρ ◆2

¯ nth C ≈ 0.4 ✓ m 1 g ◆ ✓2 kW Pcav ◆ ✓ 6000 Finesse ◆ ✓ T 300 K ◆

Reaching SNR ~ 1 at room temperature:

Close to MIT one-gram experiment m !m/2" Qm Pcav 1 g 1 Hz 106 2 kW 1 mg 10 Hz 109 2 W 1 #g 100 Hz 1012 2 mW

10 Non-relativistic limit [1]

Semi-classical Gravity: Emergent gravity [2, 3, 4]:

Gµν = 8πG c4 hψ| ˆ Tµν|ψi

ˆ HSN

AB = ~ ω2 g

2ωm ⇣ h ˆ QAi ˆ QB + ˆ QAh ˆ QBi ⌘

Zero correlation ˆ HAB = TS( ˆ QA − ˆ QB) + δ ˆ HAB

HAB = TS(h ˆ QAi h ˆ QBi)

• r

Zero correlation Reduced correlation SNR

[1] H. Yang, H. Miao, D. Lee, B. Helou, and Y. Chen, Phys. Rev. Lett. 110, 170401 (2013). [2] T. Jacobson, Phys. Rev. Lett. 75, 1260 (1995). [3] E. Verlinde, Journal of High Energy Physics 2011, 29 (2011). [4] T. Padmanabhan, Modern Physics Letters A 30, 1540007 (2015).

• v Correlation can be served as an intermediate step towards entanglement.

v Classical models of gravity predict testable levels of correlation. v Low-frequency, high-quality factor oscillators are required. v More detailed design studies of the experimental schemes are needed.

Thank you!