Quantum enhanced magnetometer and squeezed state of light tunable filter
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1 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
2 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
3 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
4 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
5 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
6 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
7 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
8 Simplified setup V.Sq LO PBS 87 RB PBS Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 7 / 42
9 Setup Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 8 / 42
10 Noise contrast vs detuning in hot 87 Rb vacuum cell Noise (db) Noise (db) F g = 2 F e =, 2 Noise vs detuning Transmission Frequency (GHz) PSR noise Noise vs quadrature angle Quadrature angle (Arb.Units) Noise (db) Noise (db) F g = F e =, 2 Noise vs detuning Transmission Frequency (GHz) PSR noise Noise vs quadrature angle Quadrature angle (Arb.Units) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 9 / 42
11 Atomic low frequency squeezing source Noise spectral density (dbm/hz) (b) (a) (b) (a) Noise Frequency (khz) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 / 42
12 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 detuning Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 / 42
13 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 ( ) detuning Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 / 42
14 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 ( ) detuning Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 / 42
15 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 ( ) detuning Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 / 42
16 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 ( ) detuning Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 / 42
17 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 χ (+ ) χ ( ) χ (+ ) χ ( ) B field detuning Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 / 42
18 Optical magnetometer and non linear Faraday effect Naive model of rotation Experiment.5 χ 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
19 Optical magnetometer and non linear Faraday effect Naive model of rotation Experiment.5 χ 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
20 Magnetometer response vs atomic density.25 Slope of rotation signal (V/µT) Normalized transmission.75 2 Atomic density (atoms/cm 3 ) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 3 / 42
21 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
22 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
23 Magnetometer noise floor improvements Noise spectral density (dbm/hz) (b) (a) (b) (a) Noise Frequency (khz) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 6 / 42
24 Magnetometer noise spectra Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 7 / 42
25 Noise suppression and response vs atomic density Noise suppression Noise suppression (db) khz khz 5 khz MHz 6 2 Atomic density (atoms/cm 3 ).25 Response Slope of rotation signal (V/µT) Normalized transmission.75 2 Atomic density (atoms/cm 3 ) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 8 / 42
26 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
27 Light group velocity expression Susceptibility Group velocity v g = c ω n ω χ χ Rotation vs B field detuning Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 2 / 42
28 Light group velocity expression Group velocity v g = c ω n ω Susceptibility Rotation vs B field.5 χ χ.5 χ detuning B field Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 2 / 42
29 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
30 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
31 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 Magnetic field (G) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, / 42
32 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 SNL (a) (b) (c) SNL time (µs) (d) (e) (f).5.5 time (ms) Noise power (db) 5 5 (a) antisqueezed (b) squeezed Magnetic field (G) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, / 42
33 Time advancement setup Eugeniy E. Mikhailov (W&M) Squeezed light October 5, / 42
34 Squeezing modulation and time advancement Eugeniy E. Mikhailov (W&M) Squeezed light October 5, / 42
35 Squeezing after advancement cell Eugeniy E. Mikhailov (W&M) Squeezed light October 5, / 42
36 Advancement vs power Eugeniy E. Mikhailov (W&M) Squeezed light October 5, / 42
37 Advancement vs power Eugeniy E. Mikhailov (W&M) Squeezed light October 5, / 42
38 Quantum limited interferometers revisited Vacuum input Squeezed input laser laser Eugeniy E. Mikhailov (W&M) Squeezed light October 5, / 42
39 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, / 42
40 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, / 42
41 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, / 42
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, / 42
43 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, / 42
44 EIT filter Probe transparency dependence on its detuning. a Transparency [Arb. Unit] ω p Probe detuning [Arb. Unit] c b ω bc Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 3 / 42
45 EIT filter Probe transparency dependence on its detuning. a Probe transparency dependence on its detuning. Transparency [Arb. Unit] ω p ω d Transparency [Arb. Unit] Probe detuning [Arb. Unit] b ω bc c Probe detuning [Arb. Unit] Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 3 / 42
46 Squeezing and EIT filter ( V out V out 2 ) ( A 2 = + A 2 A 2 A 2 + ) ( V in V in 2 ) [ ( )] ( + A 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 ±](/docs-images/86/93318097/images/47-0.jpg "= 2 (Θ + ± Θ ) A ± = 2 (T + ± T ) a ω p ω d c b ω bc Eugeniy E.")
47 Squeezing and EIT filter ( V out V out 2 ) ( A 2 = + A 2 A 2 A 2 + ) ( V in V in 2 ) [ ( )] ( + A 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
48 Squeezing and EIT filter ( V out V out 2 ) ( A 2 = + A 2 A 2 A 2 + ) ( V in V in 2 ) [ ( )] ( + A 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 ±](/docs-images/86/93318097/images/49-0.jpg "= 2 (Θ + ± Θ ) A ± = 2 (T + ± T ) a ω p ω d c b ω bc Eugeniy E.")
49 Squeezing and EIT filter ( V out V out 2 ) ( A 2 = + A 2 A 2 A 2 + ) ( V in V in 2 ) [ ( )] ( + A 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
50 Squeezing and EIT filter setup Eugeniy E. Mikhailov (W&M) Squeezed light October 5, / 42
51 Squeezing and EIT filter setup Eugeniy E. Mikhailov (W&M) Squeezed light October 5, / 42
52 EIT filter and measurements without light Transmission (Arb. Units) Noise Frequency (MHz) Signal in the noise quadratures Coherent signal ωp b ω bc a ω d c Noise Frequency (MHz) Noise Frequency (MHz) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, / 42 Noise power (dbm) Noise power (dbm)
53 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 A2 X ) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, / 42
54 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) Input 6 Input Noise(dB) 4 Noise(dB) output output Frequency (MHz) Frequency (MHz) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, / 42
55 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) Input 6 Input Noise (db) 4 2 output Noise (db) 4 2 output Noise frequency (MHz) Frequency (MHz) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, / 42
56 Excess noise and leakage Effect of leakage photons Shot noise Output noise, mv leakage Output noise, 2 mv leakage db MHz Eugeniy E. Mikhailov (W&M) Squeezed light October 5, / 42
57 Theoretical prediction for MOT squeezing with 87 Rb F g = 2 F e =, 2 high optical density is very important γ = - Γ 87 Rb D Rabi = 3 Γ squeezing antisqueezing 2 6 γ = -2 Γ F=2 to F'= F=2 to F'=2-8 F=2 to F'= F=2 to F'=2 Normalized noise power (db) γ = -3 Γ Optical density: γ = -4 Γ -8 F=2 to F'= F=2 to F'=2-8 F=2 to F'= F=2 to F'= Laser detuning (MHz) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, / 42
58 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, / 42
59 Noise contrast in MOT with 87 Rb F g = 2 F e = Noise (db) (a) (b) Quadrature angle (Arb. Units) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, / 42
60 Squeezing in MOT with 87 Rb F g = 2 F e = Noise (db).2 (a) (b) -.4 Quadrature angle (Arb. Units) Eugeniy E. Mikhailov (W&M) Squeezed light October 5, 22 4 / 42
61 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
62 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: Support from Eugeniy E. Mikhailov (W&M) Squeezed light October 5, / 42
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