Squeezed States of Light

Roman Schnabel

Albert-Einstein-Institut (AEI)

Institut für Gravitationsphysik

Leibniz Universität Hannover Photo-Electric Current Photo diode

A (modulation) signal?

N Photons per time interval

Time intervals

Roman Schnabel, 17 / June/ 2013 Albert - Einstein- Institut 2 Photo-Electric Current Photo diode

No signal, but photon shot noise?

N Photons per time interval

Time intervals

Roman Schnabel, 17 / June/ 2013 Albert - Einstein- Institut 3 Photon Counting Statistics

Coherent state " = 100 2 " Nˆ = N = # =10000 1 1 Relative shot-noise ~ ~ N PLaser N ! + NNNN Probability [rel. units]

Photon number N

Roman Schnabel, 17 / June/ 2013 Albert - Einstein- Institut 4
Squeezed Counting Statistics

Squeezing factor: 10 dB Noise squeezing

Squeezing factor: 3 dB Probability [rel. units]

Photon number N

Roman Schnabel, 17 / June/ 2013 Albert - Einstein- Institut 5 Photo-Electric Current – Squeezed

Broadband squeezing

N Photons per time interval

Time intervals

Roman Schnabel, 17 / June/ 2013 Albert - Einstein- Institut 6 Squeezing of Interferometer Shot-Noise

C. M. Caves (1981): Reduction of quantum noise with squeezed light

High power laser

Squeezed Faraday light laser Rotator Photo diode

[Caves, Phys. Rev. D 23, 1693 (1981)]

Roman Schnabel, 17 / June/ 2013 Albert - Einstein- Institut 7 Wigner Function of Squeezed Light

Phase-space quasi- probability distribution of a squeezed vacuum state, ! = 5 MHz

[Mehmet et al., PRA 81, 013814 (2010)]

!2 " !" X1( , ) = = # 2 vac 0, 07 ˆ 11.6 dB! ! X1 (", !")

Roman Schnabel, 17 / June/ 2013 Albert - Einstein- Institut 8 Generation of Squeezed Light (PDC)

Pump field input (cw, 532nm)

"2-nonlinear crystal: MgO:LiNbO3 Squeezed field output (cw, 1064nm) by parametric down-conversion (PDC)

Standing wave cavity

Roman Schnabel, 17 / June/ 2013 Albert - Einstein- Institut 9 Detection of Squeezed States

Resonator for laser frequency f0#

Pump- light, 2f0# Squeezed light composed of photon pairs, f0! Photograph of the optical resonator components for squeezing generation Balanced via parametric down conversion. Bright homodyne detector Crystal: PPKTP or MgO:LiNbO3 field, f0 (LO)# $0# fFou# %f =1Hz!

Roman Schnabel, 17 / June/ 2013 Albert - Einstein- Institut 1 0 Generation of Squeezed Light

[J. Bauchrowitz, T. Westphal, RS, Am. J. Phys. (2013), accepted]

Roman Schnabel, 17 / June/ 2013 Albert - Einstein- Institut 1 1 Squeezed States (Overview)

",# , # = r$ ei% Squeezing parameter and angle

' 1 * 2 †2 * Squeezing operator producing 0,# = Sˆ (#) 0 = exp) (# aˆ & #aˆ ), 0 ( 2 + squeezed vacuum

1 & 1 ",# -2 Xˆ ",# = e 2r , ",# -2 Xˆ ",# = e2r Quadrature variances 1 4 2 4 Sˆ †()# aˆ Sˆ ()# = aˆ coshr & aˆ †ei% sinhr Sˆ †()# aˆ † Sˆ ()# = aˆ † coshr & aˆ e&i% sinhr (aˆ coshr + aˆ †ei% sinhr) ",# = (" coshr + " *ei% sinhr) ",# Eigenwert equation ˆ ˆ . 0,# = 0,# 0,# , m . 0,# n / .0,# ,m,n = ... Density matrix element ˆ in Fock basis 2m +1 . 0,# 2m +1 = 0 2m ()2m ! ()tanhr 2m .ˆ # 2m = 2 0, 22m ()m! coshr

Roman Schnabel, 17 / June/ 2013 Albert - Einstein- Institut 1 2

“Squeezing” Laboratories

First squeezed light: [Slusher et al., PRL 55, 2409 (1985)]

Research labs with squeezed light (not complete):

-! Kimble (CalTech): teleportation: [Furuzawa et al., SCIENCE 282, 706 (1998)] -! Grangier (Orsay); kitten: [Ourjoumtsev et al., SCIENCE, 312, 83 (2006)] -! Schiller and Mlynek (Konstanz): tomography: [Nature 387, 471 (1997)] -! Bachor and Lam (Canberra): 6dB at 1064nm [J. Opt. B 1, 469 (1999)] -! Leuchs (Erlangen); ~7 dB pulsed [Opt. Lett. 33, 116 (2008)] -! Polzik (Copenhagen), [Neergaard-Nielsen et al., PRL 97, 083604 (2006)] -! Furusawa (Tokyo); 9 dB: [Takeno et al., Opt. Express 15, 4321 (2007)] -! Fabre (Paris); Zhang, Peng (Shanxi); Andersen (Copenhagen); Mavalvala (MIT) -! Nussenzveig (Sao Paulo); Pfister (Virginia); ...

Roman Schnabel, 17 / June/ 2013 Albert - Einstein- Institut 1 3 Squeezing Issues for GW Detection

Squeezing at frequencies in the GW detection band (10 Hz to 10 kHz) -! Control beam as noise source identified [Bowen, RS et al., J. Opt. B 4, 421 (2002)], [RS et al., Opt. Comm. 240, 185 (2004)] -! First Audioband squeezing [McKenzie et al., PRL 93, 161105 (2004)] -! New control scheme [Vahlbruch, RS et al., PRL 97, 011101 (2006)] -! 6 dB over complete band [Vahlbruch, RS et al., NJP 9, 371 (2007]

Compatibility with GW detector techniques -! Power-recycling [McKenzie et al., PRL 88, 231102 (2002).] - Signal-recycling [Vahlbruch, RS et al., PRL 95, 211102 (2005)] - Suspended interferometer [Goda et al., Nat. Phys. 4, 472 (2008).]

Strong continuous wave squeezing (>10 dB) at 1064nm -! [Vahlbruch, RS et al., PRL 100, 033602 (2008)] -! [M. Mehmet, RS et al., PRA 81, 013814 (2010)]

Review: [R.S. et al., Nature Comm. 1:121 doi: 10.1038/ncomms1122 (2010)]

Roman Schnabel, 17 / June/ 2013 Albert - Einstein- Institut 1 4 2007: Squeezing Down to 1 Hz

6.5 dB squeezing

(d) Vacuum noise level, PLO= 464 µW [H. Vahlbruch et al., New J. Phys. 9, 371 (2007)] (e)! Squeezed noise, PLO= 464 µW First audio-band squeezing: (f)! Electronic dark noise [McKenzie et al., PRL 93, 161105 (2004)]

Roman Schnabel, 17 / June/ 2013 Albert - Einstein- Institut 1 5 2008: Squeezing Generation > 10 dB

99.8% visibility

Parametric down-conversion [H. Vahlbruch, RS et al., PRL 100, 033602 (2008)]

Roman Schnabel, 17 / June/ 2013 Albert - Einstein- Institut 1 6 Design of the
GEO600 Squeezer

[Henning Vahlbruch, PhD thesis, Hannover, 2008] - Gravitational Wave International Committee (GWIC) Thesis Prize 2008 - S-AMOP DPG Thesis Prize 2010

Roman Schnabel, 17 / June/ 2013 Albert - Einstein- Institut 1 7 The GEO600 Squeezed Light Laser

Alexander Khalaidovski and Henning Vahlbruch, 2009/2010 Real-time control system: Nico Lastzka and Christian Gräf

Roman Schnabel, 17 / June/ 2013 Albert - Einstein- Institut 1 8 The GEO600 Squeezed Light Laser

[H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gräf, K. Danzmann, and R. Schnabel, The GEO600 squeezed light source, Class. Quantum Grav. 27, 084027 (2010)] Alexander Khalaidovski: Stefano Braccini Thesis Prize 2011.

Roman Schnabel, 17 / June/ 2013 Albert - Einstein- Institut 1 9 Transport to the GEO600 GW Detector

Roman Schnabel, 17 / June/ 2013 Albert - Einstein- Institut 2 0 The Implementation

April 2010 – September 2010:

•! Implementation of an output mode-cleaning cavity

•! Phase lock of the Squeezed-Light Laser to the GEO600 main laser

•! Coupling into GEO600 via a low-loss Faraday rotator (custom design with <1% loss)

•! Matching of the squeezed mode to the GEO600 mode

•! Replacement of photo diode (custom design with 3mm ! and >99% quantum efficiency)

[The “GEO600 Team” led by Hartmut Grote and the “Squeezer Team” led by Henning Vahlbruch]

Roman Schnabel, 17 / June/ 2013 Albert - Einstein- Institut 2 1 GEO600: Noise without Squeezed Light Hz]

 -20 10

Observatory noise without squeezed light

-21 10 Observatory noise, calibrated to GW-strain [1/ Observatory noise, calibrated to GW-strain -22 10 400 500 800 1k 2k 5k4k3k Frequency [Hz]

Roman Schnabel, 17 / June/ 2013 Albert - Einstein- Institut 2 2 GEO600: Squeezing Enhanced Hz]



-20 [The LSC, Nat. Phys. 7, 962 (2011)] 10

Observatory noise without squeezed light

-21 10

Observatory noise with squeezed light (and loss) Observatory noise, calibrated to GW-strain [1/ Observatory noise, calibrated to GW-strain -22 10 400 500 800 1k 2k 5k4k3k Frequency [Hz]

Roman Schnabel, 17 / June/ 2013 Albert - Einstein- Institut 2 3 This is not just a proof of principle! GEO600 regularly uses squeezed light duringShot its noise observational runs.

squeezed

Roman Schnabel, 17 / June/ 2013 Albert - Einstein- Institut 2 4 1 2 3 4 5 6 7 8 9 10 11 12