Quantum enhanced magnetometer and squeezed state of light tunable filter

Quantum enhanced magnetometer and squeezed state of light tunable filter Eugeniy E. Mikhailov The College of William & Mary October 5, 22 Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 / 42

Transition from classical to quantum field Classical analog Field amplitude a Field real part X = (a + a)/2 Field imaginary part X 2 = i(a a)/2 Quantum approach Field operator â Amplitude quadrature ˆX = (â + â)/2 Phase quadrature ˆX 2 = i(â â)/2 E(φ) = a e iφ = X + ix 2 Ê(φ) = ˆX + i ˆX 2 X 2 φ X 2 φ X X Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 3 / 42

Squeezed quantum states zoo Unsqueezed coherent X 2 φ X 2 φ X X Notice X X 2 4 Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 4 / 42

Squeezed quantum states zoo Unsqueezed coherent Amplitude squeezed X 2 φ X 2 φ φ X 2 X X X Notice X X 2 4 Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 4 / 42

Squeezed quantum states zoo Unsqueezed coherent Amplitude squeezed X 2 φ X 2 φ φ X 2 X Phase squeezed X X X 2 φ Notice X X 2 4 X Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 4 / 42

Squeezed quantum states zoo Unsqueezed coherent Amplitude squeezed X 2 φ X 2 φ θ X 2 X Phase squeezed X Vacuum squeezed X X 2 X 2 φ θ Notice X X 2 4 X X Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 4 / 42

Self-rotation of elliptical polarization in atomic medium SR Ω + Ω - A.B. Matsko et al., PRA 66, 4385 (22): theoretically prediction of 4-6 db noise suppression a out = a in + igl 2 (a in a in) () Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 5 / 42

Simplified setup V.Sq LO PBS 87 RB PBS Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 7 / 42

Setup Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 8 / 42

Noise contrast vs detuning in hot 87 Rb vacuum cell Noise (db) Noise (db) F g = 2 F e =, 2 Noise vs detuning 2 8 6 4 2-2 -.4 -.2.2.4.6.8.2.4 Transmission Frequency (GHz) PSR noise Noise vs quadrature angle 8 7 6 5 4 3 2-2 3 4 5 6 7 8 9 Quadrature angle (Arb.Units) Noise (db) Noise (db) 4.5 3.5 4 2.5 3.5 2.5 -.5 - F g = F e =, 2 Noise vs detuning 6.6 6.8 7 7.2 7.4 7.6 7.8 Transmission Frequency (GHz) PSR noise Noise vs quadrature angle 8 7 6 5 4 3 2 - -2 2 4 6 8 2 Quadrature angle (Arb.Units) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 9 / 42

Atomic low frequency squeezing source Noise spectral density (dbm/hz) -68-7 -6-72 -65-74 -7-76 -75 (b) -78-8 -8-85 (a) -82.5.5 2 2.5 3 3.5 4 4.5 5 (b) -84-86 (a) 25 5 75 Noise Frequency (khz) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 / 42

Optical magnetometer based on Faraday effect 87 Rb D line F'=2 F'= m'= + - F=2 F= m=- m= m= Susceptibility vs B.5 χ χ -.5 - - -5 5 detuning Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 / 42

Optical magnetometer based on Faraday effect 87 Rb D line F'=2 F'= m'= + - F=2 F= m=- m= m= Susceptibility vs B.5 χ (+ ) χ ( ) χ (+ ) χ ( ) -.5 - - -5 5 detuning Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 / 42

Optical magnetometer based on Faraday effect 87 Rb D line F'=2 F'= m'= + - F=2 F= m=- m= m= Susceptibility vs B.5 χ (+ ) χ ( ) χ (+ ) χ ( ) -.5 - - -5 5 detuning Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 / 42

Optical magnetometer based on Faraday effect 87 Rb D line F'=2 F'= m'= + - F=2 F= m=- m= m= Susceptibility vs B.5 χ (+ ) χ ( ) χ (+ ) χ ( ) -.5 - - -5 5 detuning Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 / 42

Optical magnetometer based on Faraday effect 87 Rb D line F'=2 F'= m'= + - F=2 F= m=- m= m= Susceptibility vs B.5 χ (+ ) χ ( ) χ (+ ) χ ( ) -.5 - - -5 5 detuning Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 / 42

Optical magnetometer based on Faraday effect 87 Rb D line F'=2 F'= m'= + - Polarization rotation vs B F=2 F= m=- m= m=.5 χ Susceptibility vs B.5 -.5 χ (+ ) χ ( ) χ (+ ) χ ( ) -.5 - - -5 5 B field - - -5 5 detuning Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 / 42

Optical magnetometer and non linear Faraday effect Naive model of rotation Experiment.5 χ -.5 - - -5 5 B field SMPM FIBER LENS LASER λ/2 GP MAGNETIC B Rb Cell Rb Cell 87 Rb SHIELDING SCOPE LENS BPD λ/2 PBS Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 2 / 42

Optical magnetometer and non linear Faraday effect Naive model of rotation Experiment.5 χ -.5 - - -5 5 B field SMPM FIBER LENS LASER λ/2 GP MAGNETIC B Rb Cell Rb Cell 87 Rb SHIELDING SCOPE LENS BPD λ/2 PBS Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 2 / 42

Magnetometer response vs atomic density.25 Slope of rotation signal (V/µT).2.5..5.95.9.85.8 Normalized transmission.75 2 Atomic density (atoms/cm 3 ) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 3 / 42

Shot noise limit of the magnetometer SMPM FIBER LENS LASER λ/2 GP Rb Cell MAGNETIC B Rb Cell 87 Rb SHIELDING SCOPE LENS λ/2 BPD PBS Scope S = E p + E v 2 E p E v 2 S = 4E p E v < S > E p < E v > E p E v Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 4 / 42

Squeezed enhanced magnetometer setup SMPM FIBER SQUEEZER MAGNETOMETER SCOPE LENS GP LENS LENS BPD x y k z λ/2 Rb Cell Rb Cell PhR λ/2 PBS PBS Sq. Vac x y z k (a) Laser Field Sq. Vac (b) x y Laser Field Note: Squeezed enhanced magnetometer was first demonstrated by Wolfgramm et. al Phys. Rev. Lett, 5, 536, 2. Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 5 / 42

Magnetometer noise floor improvements Noise spectral density (dbm/hz) -68-7 -6-72 -65-74 -7-76 -75 (b) -78-8 -8 (a) -85-82.5.5 2 2.5 3 3.5 4 4.5 5 (b) -84-86 (a) 25 5 75 Noise Frequency (khz) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 6 / 42

Magnetometer noise spectra Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 7 / 42

Noise suppression and response vs atomic density Noise suppression Noise suppression (db) 2 2 4 5 khz khz 5 khz MHz 6 2 Atomic density (atoms/cm 3 ).25 Response Slope of rotation signal (V/µT).2.5..5.95.9.85.8 Normalized transmission.75 2 Atomic density (atoms/cm 3 ) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 8 / 42

Magnetometer with squeezing enhancement SMPM FIBER LENS LASER GP SQUEEZER MAGNETIC MAGNETOMETER MAGNETIC SCOPE LENS BPD λ/2 Rb Cell 87 Rb SHIELDING Rb Cell 87 λ/4 Rb λ/2 PBS SHIELDING PBS Sensitivity pt/ Hz (a) (b) coherent probe squeezed probe 2 Atomic density (atoms/cm 3 ) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 9 / 42

Light group velocity expression Susceptibility Group velocity v g = c ω n ω.5 -.5 χ χ Rotation vs B field - - -5 5 detuning Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 2 / 42

Light group velocity expression Group velocity v g = c ω n ω Susceptibility Rotation vs B field.5 χ χ.5 χ -.5 -.5 - - -5 5 detuning - - -5 5 B field Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 2 / 42

Light group velocity estimate Group velocity v g = c ω n ω Delay τ = L v g n ω R B Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 2 / 42

Light group velocity estimate Group velocity v g = c ω n ω Delay τ = L v g n ω R B Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 2 / 42

Squeezing vs magnetic field Spectrum analyzer settings: Central frequency = MHz, VBW = 3 MHz, RBW = khz 5 (a) antisqueezed SMPM FIBER LENS LASER λ/2 GP MAGNETIC B Rb Cell Rb Cell 87 Rb SHIELDING SCOPE LENS BPD λ/2 PBS Noise power (db) 5 (b) squeezed.5..5.5 2 2.5 5.2.4.6.8.2 Magnetic field (G) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 22 / 42

Squeezing vs magnetic field Spectrum analyzer settings: Central frequency = MHz, VBW = 3 MHz, RBW = khz B field (G) Noise (db) B field (G) Noise (db) B field (G) Noise (db). SNL 2.5.5. SNL 2.5.5. (a) (b) (c) SNL 2 2 2 time (µs) (d) (e) (f).5.5 time (ms) Noise power (db) 5 5 (a) antisqueezed (b) squeezed.5..5.5 2 2.5 5.2.4.6.8.2 Magnetic field (G) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 22 / 42

Time advancement setup Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 23 / 42

Squeezing modulation and time advancement Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 24 / 42

Squeezing after advancement cell Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 25 / 42

Advancement vs power Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 26 / 42

Advancement vs power Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 26 / 42

Quantum limited interferometers revisited Vacuum input Squeezed input laser laser Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 27 / 42

Limiting noise - Quantum Optical noise Next generation of LIGO will be quantum optical noise limited at almost all detection frequencies. Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 28 / 42

Limiting noise - Quantum Optical noise Next generation of LIGO will be quantum optical noise limited at almost all detection frequencies. shot noise Uncertainty in number of photons h P (2) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 28 / 42

Limiting noise - Quantum Optical noise Next generation of LIGO will be quantum optical noise limited at almost all detection frequencies. shot noise Uncertainty in number of photons h P (2) radiation pressure noise Photons impart momentum to mirrors P h M 2 f 4 (3) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 28 / 42

Limiting noise - Quantum Optical noise Next generation of LIGO will be quantum optical noise limited at almost all detection frequencies. shot noise Uncertainty in number of photons h P (2) radiation pressure noise Photons impart momentum to mirrors P h M 2 f 4 (3) There is no optimal light power to suit all detection frequency. Optimal power depends on desired detection frequency. Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 28 / 42

Interferometer sensitivity improvement with squeezing Projected advanced LIGO sensitivity F. Ya. Khalili Phys. Rev. D 8, 222 (2) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 29 / 42

EIT filter Probe transparency dependence on its detuning. a Transparency [Arb. Unit].8.6.4.2 ω p - -5 5 Probe detuning [Arb. Unit] c b ω bc Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 3 / 42

EIT filter Probe transparency dependence on its detuning. a Probe transparency dependence on its detuning. Transparency [Arb. Unit].8.6.4.2 ω p ω d Transparency [Arb. Unit].8.6.4.2 - -5 5 Probe detuning [Arb. Unit] b ω bc c - -5 5 Probe detuning [Arb. Unit] Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 3 / 42

Squeezing and EIT filter ( V out V out 2 ) ( A 2 = + A 2 A 2 A 2 + ) ( V in V in 2 ) [ ( )] ( + A 2 + + A 2 ) ϕ ± = 2 (Θ + ± Θ ) A ± = 2 (T + ± T ) a ω p ω d c b ω bc Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 3 / 42

Squeezing and EIT filter ( V out V out 2 ) ( A 2 = + A 2 A 2 A 2 + ) ( V in V in 2 ) [ ( )] ( + A 2 + + A 2 ) ϕ ± = 2 (Θ + ± Θ ) A ± = 2 (T + ± T ) a ω p ω d c b ω bc Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 3 / 42

Squeezing and EIT filter ( V out V out 2 ) ( A 2 = + A 2 A 2 A 2 + ) ( V in V in 2 ) [ ( )] ( + A 2 + + A 2 ) ϕ ± = 2 (Θ + ± Θ ) A ± = 2 (T + ± T ) a ω p ω d c b ω bc Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 3 / 42

Squeezing and EIT filter ( V out V out 2 ) ( A 2 = + A 2 A 2 A 2 + ) ( V in V in 2 ) [ ( )] ( + A 2 + + A 2 ) ϕ ± = 2 (Θ + ± Θ ) A ± = 2 (T + ± T ) a ω p ω d c b ω bc Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 3 / 42

Squeezing and EIT filter setup Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 32 / 42

Squeezing and EIT filter setup Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 32 / 42

EIT filter and measurements without light Transmission (Arb. Units).65.6.55.5.45.4.35.3.25-2 -.5 - -.5.5.5 2 Noise Frequency (MHz) Signal in the noise quadratures Coherent signal ωp b ω bc a ω d c 4 4 2 2 8 8 6 6 4 4 2 2-2 -2-4 -4.5.5 2.5.5 2 Noise Frequency (MHz) Noise Frequency (MHz) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 33 / 42 Noise power (dbm) Noise power (dbm)

Squeezing angle rotation θ θ X 2 X 2 ( V out V out 2 ) = X Locked at 3kHz ( cos 2 ϕ + sin 2 ϕ + sin 2 ϕ + cos 2 ϕ + ) ( A 2 + A 2 A 2 A2 + ) ( V in V in 2 Locked at 2kHz ) [ ( )] ( + A 2 + + A2 X ) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 34 / 42

Narrower filter T=35 C, no control transmission 42% T=4 C, no control transmission 7% Noise vs frequency through atoms: control off (35 degrees) Noise vs frequency through atoms: control off (4 degrees) 8 8 6 Input 6 Input Noise(dB) 4 Noise(dB) 4 2 2 output output 2.2.4.6.8 Frequency (MHz) 2.2.4.6.8 Frequency (MHz) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 35 / 42

Narrower filter T=35 C, no control transmission 42% T=4 C, no control transmission 7% Noise vs frequency through EIT (35 degrees) Noise vs frequency through EIT (4 degrees) 8 8 6 Input 6 Input Noise (db) 4 2 output Noise (db) 4 2 output 2.2.4.6.8 Noise frequency (MHz) 2.2.4.6.8 Frequency (MHz) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 35 / 42

Excess noise and leakage Effect of leakage photons 6 4 2 Shot noise Output noise, mv leakage Output noise, 2 mv leakage db 8 6 4 2 2.5.5 2 MHz Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 36 / 42

Theoretical prediction for MOT squeezing with 87 Rb F g = 2 F e =, 2 high optical density is very important 24 24 2 6 γ = - Γ 87 Rb D Rabi = 3 Γ squeezing antisqueezing 2 6 γ = -2 Γ 2 2 8 8 4 4-4 -4-8 F=2 to F'= F=2 to F'=2-8 F=2 to F'= F=2 to F'=2 Normalized noise power (db) 24 2 6 2 8 4-4 - -5 5 5 γ = -3 Γ 24 2 6 2 8 4-4 - -5 5 5 Optical density: 5 9 3 7 γ = -4 Γ -8 F=2 to F'= F=2 to F'=2-8 F=2 to F'= F=2 to F'=2 - -5 5 5 - -5 5 5 Laser detuning (MHz) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 37 / 42

MOT squeezer Cloud size = mm, T = 2 µk, N = 7 9 /cm 3, OD = 2, beam size =. mm, 5 interacting atoms V.Sq LO PBS PBS Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 38 / 42

Noise contrast in MOT with 87 Rb F g = 2 F e = Noise (db).9.8.7.6.5.4.3.2. -. (a) (b) Quadrature angle (Arb. Units) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 39 / 42

Squeezing in MOT with 87 Rb F g = 2 F e = Noise (db).2 (a)..8.6.4.2 -.2 (b) -.4 Quadrature angle (Arb. Units) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 4 / 42

People Travis Horrom and Gleb Romanov Robinjeet Singh, LSU Irina Novikova Jonathan P. Dowling, LSU Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 4 / 42

Summary We demonstrate fully atomic squeezed enhanced magnetometer Magnetometer noise floor lowered in the range from several khz to several MHz Demonstrated sensitivity as low as pt/ Hz in our particular setup First demonstration of superluminal squeezing propagation with v g = c/2 or time advancement of.5 µs For more details: T. Horrom, et al. Quantum Enhanced Magnetometer with Low Frequency Squeezing, PRA, 86, 2383, (22). T. Horrom, et al. All-atomic generation and noise-quadrature filtering of squeezed vacuum in hot Rb vapor, arxiv:24.3967. Support from Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 42 / 42