Squeezed states of light - generation and applications
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1 Squeezed states of light - generation and applications Eugeniy E. Mikhailov The College of William & Mary Fudan, December 24, 2013 Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
2 People Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
3 From ray optics to semiclassical optics Classical/Geometrical optics light is a ray which propagates straight cannot explain diffraction and interference Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
4 From ray optics to semiclassical optics Classical/Geometrical optics light is a ray which propagates straight cannot explain diffraction and interference Semiclassical optics light is a wave color (wavelength/frequency) is important amplitude (a) and phase are important, E(t) = ae i(kz ωt) cannot explain residual measurements noise Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
5 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz Detectors sense the real part of the field ( ) but there is a way to see as well Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
6 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
7 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
8 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
9 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
10 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
11 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
12 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
13 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
14 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
15 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
16 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
17 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
18 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
19 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
20 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
21 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
22 Classical quadratures vs time in a rotating frame E() = a e i = a cos() + i a sin() = + i, = ωt kz Projection t Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
23 Reality check quadratures vs time E() = a e i = a cos() + i a sin() = + i, = ωt kz Projection t Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
24 Detector quantum noise Simple photodetector N V V N V N Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
25 Detector quantum noise Simple photodetector Balanced photodetector N V 2N 50/50 N V N V N N V = 0 V V N Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
26 Transition from classical to quantum field Classical analog Field amplitude a Field real part = (a + a)/2 Field imaginary part = i(a a)/2 Quantum approach Field operator â Amplitude quadrature ˆ = (â + â)/2 Phase quadrature ˆ = i(â â)/2 E() = a e i = + i Ê() = ˆ + i ˆ Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
27 Quantum optics summary Light consist of photons ˆN = a a Commutator relationship [a, a ] = 1 [, ] = i/2 Detectors measure number of photons ˆN Quadratures ˆ and ˆ Uncertainty relationship 1/4 Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
28 Heisenberg uncertainty principle and its optics equivalent Heisenberg uncertainty principle p x /2 The more precisely the POSITION is determined, the less precisely the MOMENTUM is known, and vice versa Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
29 Heisenberg uncertainty principle and its optics equivalent Heisenberg uncertainty principle p x /2 The more precisely the POSITION is determined, the less precisely the MOMENTUM is known, and vice versa Optics equivalent N 1 The more precisely the PHASE is determined, the less precisely the AMPLITUDE is known, and vice versa Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
30 Heisenberg uncertainty principle and its optics equivalent Heisenberg uncertainty principle p x /2 The more precisely the POSITION is determined, the less precisely the MOMENTUM is known, and vice versa Optics equivalent N 1 The more precisely the PHASE is determined, the less precisely the AMPLITUDE is known, and vice versa Optics equivalent strict definition 1/4 Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
31 Coherent state is minimum uncertainty state = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
32 Coherent state is minimum uncertainty state = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
33 Coherent state is minimum uncertainty state = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
34 Coherent state is minimum uncertainty state = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
35 Coherent state is minimum uncertainty state = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
36 Coherent state is minimum uncertainty state = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
37 Coherent state is minimum uncertainty state = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
38 Coherent state is minimum uncertainty state = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
39 Coherent state is minimum uncertainty state = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
40 Coherent state is minimum uncertainty state = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
41 Coherent state is minimum uncertainty state = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
42 Coherent state is minimum uncertainty state = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
43 Coherent state is minimum uncertainty state = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
44 Coherent state is minimum uncertainty state = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
45 Coherent state is minimum uncertainty state = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
46 Coherent state is minimum uncertainty state = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
47 Amplitude squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
48 Amplitude squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
49 Amplitude squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
50 Amplitude squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
51 Amplitude squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
52 Amplitude squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
53 Amplitude squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
54 Amplitude squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
55 Amplitude squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
56 Amplitude squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
57 Amplitude squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
58 Amplitude squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
59 Amplitude squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
60 Amplitude squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
61 Amplitude squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
62 Amplitude squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
63 Phase squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
64 Phase squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
65 Phase squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
66 Phase squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
67 Phase squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
68 Phase squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
69 Phase squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
70 Phase squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
71 Phase squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
72 Phase squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
73 Phase squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
74 Phase squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
75 Phase squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
76 Phase squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
77 Phase squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
78 Phase squeezed states = 1/4 Projection 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
79 Squeezed quantum states zoo Unsqueezed coherent Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
80 Squeezed quantum states zoo Unsqueezed coherent Amplitude squeezed Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
81 Squeezed quantum states zoo Unsqueezed coherent Amplitude squeezed Phase squeezed Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
82 Squeezed quantum states zoo Unsqueezed coherent Amplitude squeezed θ Phase squeezed Vacuum squeezed θ Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
83 Squeezed field generation recipe Take a vacuum state 0 > H = 1 2 Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
84 Squeezed field generation recipe Take a vacuum state 0 > Apply squeezing operator ξ >= Ŝ(ξ) 0 > Ŝ(ξ) = e 1 2 ξ a ξa 2 θ H = 1 2 Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
85 Squeezed field generation recipe Take a vacuum state 0 > Apply squeezing operator ξ >= Ŝ(ξ) 0 > Apply displacement operator α, ξ >= ˆD(α) s > Ŝ(ξ) = e 1 2 ξ a ξa 2 ˆD(α) = e αa α a θ H = 1 2 < α, ξ α, ξ > = Re(α), < α, ξ α, ξ > = Im(α) Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
86 Squeezed field generation recipe Take a vacuum state 0 > Apply squeezing operator ξ >= Ŝ(ξ) 0 > Apply displacement operator α, ξ >= ˆD(α) s > Ŝ(ξ) = e 1 2 ξ a ξa 2 ˆD(α) = e αa α a θ H = 1 2 Notice = 1 4 < α, ξ α, ξ > = Re(α), < α, ξ α, ξ > = Im(α) Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
87 Squeezed state ξ >= Ŝ(ξ) 0 > properties θ If θ = 0 Ŝ(ξ) = e 1 2 ξ a ξa 2, ξ = re iθ < ξ ( ) 2 ξ > = 1 4 e 2r < ξ ( ) 2 ξ > = 1 4 e2r < ξ ( ) 2 ξ > = 1 4 (cosh2 r + sinh 2 r 2 sinh r cosh r cos θ) < ξ ( ) 2 ξ > = 1 4 (cosh2 r + sinh 2 r + 2 sinh r cosh r cos θ) Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
88 Photon number of squeezed state ξ > Probability to detect given number of photons C =< n ξ > for squeezed vacuum even θ C 2m = ( 1) odd (2m)! 2 m m! C 2m+1 = 0 (e iθ tanh r) m cosh r Average number of photons in general squeezed state < α, ξ a a α, ξ >= α + sinh 2 r Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
89 Tools for squeezing Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
90 Tools for squeezing Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
91 Tools for squeezing 2ω b b a ω ω Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
92 Two photon squeezing picture Squeezing operator Ŝ(ξ) = e 1 2 ξ a ξa 2 Parametric down-conversion in crystal Ĥ = i χ (2) (a 2 b a 2 b) 2ω b b a ω ω Squeezing result of correlation of upper and lower sidebands Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
93 Squeezer appearance Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
94 Squeezer appearance Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
95 Squeezer appearance Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
96 Possible squeezing applications improvements any shot noise limited optical sensors noiseless signal amplification photon pair generation, entanglement, true single photon sources interferometers sensitivity boost (for example gravitational wave antennas) light free measurements quantum memory probe and information carrier Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
97 Squeezing and interferometer Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
98 Squeezing and interferometer Vacuum input laser Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
99 Squeezing and interferometer Vacuum input Squeezed input laser laser Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
100 Laser Interferometer Gravitational-wave Observatory L = 4 km h L m Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
101 Squeezing level vs time (unlocked) A quantum-enhanced prototype gravitational-wave detector, Nature Physics, 4, , (2008). Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
102 GW 40m detector and squeezer Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
103 GW 40m detector with 4dB of squeezed vacuum Signal to noise improvement by factor of 1.43 Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
104 Cavity parameters with squeezing Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
105 Cavity parameters with squeezing Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
106 Cavity parameters with squeezing OC1 OC2 PDH Servo AOM EOM TEST CAVITY PZT2 Nd:YAG LASER SQZ FI PZT1 HD1 BS HD2 S PD SA NL Servo Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
107 Cavity parameters with squeezing Nd:YAG LASER PZT1 OC1 AOM SQZ NL Servo OC2 EOM TEST CAVITY FI HD1 BS PDH Servo HD2 PZT2 S PD SA Quadrature Variance w.r.t. Shot Noise (db) Frequency (MHz) Noninvasive measurements of cavity parameters by use of squeezed vacuum, Physical Review A, 74, , (2006). Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
108 Summary for crystal squeezing Pros Cons mainstream: many different nonlinear crystals available so far the best squeezers maximum squeezing value detected 11.5 db at 1064 nm Moritz Mehmet, Henning Vahlbruch, Nico Lastzka, Karsten Danzmann, and Roman Schnabel, Observation of squeezed states with strong photon-number oscillations, Phys. Rev. A 81, (2010) well understood crystals have limited transparency window thus squeezing is hard to generate at visible wavelength at 795 nm only 4-6 db squeezing is reported this limits applications of such squeezers for spectroscopy Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
109 Self-rotation of elliptical polarization in atomic medium SR Ω + Ω - A.B. Matsko et al., PRA 66, (2002): 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 Fudan, December 24, / 70
110 Self-rotation of elliptical polarization in atomic medium SR c> d> Ω ω 0 α ω ω α 0 0 ω+ω Ω ω 0 +> > A.B. Matsko et al., PRA 66, (2002): 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 Fudan, December 24, / 70
111 Setup V.Sq LO PBS 87 RB PBS Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
112 Noise contrast vs detuning in hot 87 Rb vacuum cell Noise (db) Noise (db) F g = 2 F e = 1, 2 Noise vs detuning Transmission Frequency (GHz) PSR noise Noise vs quadrature angle Quadrature angle (Arb.Units) Noise (db) Noise (db) F g = 1 F e = 1, 2 Noise vs detuning Transmission Frequency (GHz) PSR noise Noise vs quadrature angle Quadrature angle (Arb.Units) Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
113 Squeezing region Squeezing Anti-squeezing Observation of reduction of quantum noise below the shot noise limit is corrupted by the excess noise due to atomic interaction with atoms. Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
114 Maximally squeezed spectrum with 87 Rb W&M team. 87 Rb F g = 2 F e = 2, laser power 7 mw, T=65 C Noise (db) Frequency (MHz) Lezama et.al report 3 db squeezing in similar setup Phys. Rev. A 84, (2011) Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
115 Optical magnetometer based on Faraday effect 87 Rb D 1 line F'=2 F'=1 m'=0 + - F=2 F=1 m=-1 m=0 m=1 Susceptibility vs B χ χ detuning Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
116 Optical magnetometer based on Faraday effect 87 Rb D 1 line F'=2 F'=1 m'=0 + - F=2 F=1 m=-1 m=0 m=1 Susceptibility vs B χ (+ ) χ ( ) χ (+ ) χ ( ) detuning Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
117 Optical magnetometer based on Faraday effect 87 Rb D 1 line F'=2 F'=1 m'=0 + - F=2 F=1 m=-1 m=0 m=1 Susceptibility vs B χ (+ ) χ ( ) χ (+ ) χ ( ) detuning Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
118 Optical magnetometer based on Faraday effect 87 Rb D 1 line F'=2 F'=1 m'=0 + - F=2 F=1 m=-1 m=0 m=1 Susceptibility vs B χ (+ ) χ ( ) χ (+ ) χ ( ) detuning Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
119 Optical magnetometer based on Faraday effect 87 Rb D 1 line F'=2 F'=1 m'=0 + - F=2 F=1 m=-1 m=0 m=1 Susceptibility vs B χ (+ ) χ ( ) χ (+ ) χ ( ) detuning Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
120 Optical magnetometer based on Faraday effect 87 Rb D 1 line F'=2 F'=1 m'=0 + - Polarization rotation vs B F=2 F=1 m=-1 m=0 m= χ Susceptibility vs B χ (+ ) χ ( ) χ (+ ) χ ( ) B field detuning Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
121 Optical magnetometer and non linear Faraday effect Naive model of rotation Experiment 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 Fudan, December 24, / 70
122 Optical magnetometer and non linear Faraday effect Naive model of rotation Experiment 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 Fudan, December 24, / 70
123 Magnetometer response vs atomic density Slope of rotation signal (V/µT) Normalized transmission Atomic density (atoms/cm 3 ) Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
124 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 Fudan, December 24, / 70
125 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, 105, , Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
126 Magnetometer noise floor improvements Noise spectral density (dbm/hz) (b) (a) (b) (a) Noise Frequency (khz) Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
127 Magnetometer noise spectra Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
128 Noise suppression and response vs atomic density Noise suppression Noise suppression (db) khz 100 khz 500 khz 1 MHz Atomic density (atoms/cm 3 ) Response Slope of rotation signal (V/µT) Normalized transmission Atomic density (atoms/cm 3 ) Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
129 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 Atomic density (atoms/cm 3 ) Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
130 Squeezing vs magnetic field Spectrum analyzer settings: Central frequency = 1 MHz, VBW = 3 MHz, RBW = 100 khz 15 (a) antisqueezed SMPM FIBER LENS LASER λ/2 GP Rb Cell MAGNETIC B Rb Cell 87 Rb SHIELDING SCOPE LENS λ/2 BPD PBS Noise power (db) (b) squeezed Magnetic field (G) Travis Horrom et al. "All-atomic source of squeezed vacuum with full pulse-shape control", Journal of Physics B: Atomic, Molecular and Optical Physics, Issue 12, 45, , (2012) Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
131 Squeezing vs magnetic field Spectrum analyzer settings: Central frequency = 1 MHz, VBW = 3 MHz, RBW = 100 khz B field (G) Noise (db) B field (G) Noise (db) B field (G) Noise (db) SNL SNL (a) (b) (c) 0 SNL time (µs) (d) (e) (f) time (ms) Noise power (db) (a) antisqueezed (b) squeezed Magnetic field (G) Travis Horrom et al. "All-atomic source of squeezed vacuum with full pulse-shape control", Journal of Physics B: Atomic, Molecular and Optical Physics, Issue 12, 45, , (2012). Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, /
132 Time advancement setup Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
133 Squeezing modulation and time advancement (i) Noise power, db (b) (a) Time, ms Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
134 Squeezing modulation and time advancement (ii) (iii) Normalized noise power, arb. units (b) (a) (a) (b) Time, µs Time, µs Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
135 Advancement vs power Rotation slope, rad/g Pump power, mw Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
136 Advancement vs power Rotation slope, rad/g Pump power, mw T, µs advanced squeezed Pump power, mw Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
137 Squeezing level before and after advancement cell 1.5 Noise power, db (b) (a) Pump power, mw Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
138 Squeezing advancement vs atomic density 12 Squeezing advancement, µs Rb density, cm 3 Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
139 Why superluminal squeezing? Quantum memories M. S. Shahriar, et al. Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light, Phys. Rev. A 75(5), , Yakir Aharonov, et al. Quantum Limitations on Superluminal Propagation, Phys. Rev. Lett. 81, 2190 (1998) Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
140 Squeezing and self-focusing Vortex beam (a) 1 (b) Eugeniy E. Mikhailov (W&M) (c) 1 4 (d) Power, mw Squeezed light 16 4 Waist ratio, w/wo 1.6 Density, 1012/cm cm cm cm cm Quadrature noise, db Density, 1012/cm cm cm cm cm 3 Gaussian beam Power, mw 16 Fudan, December 24, / 70
141 Quantum limited interferometers revisited Vacuum input Squeezed input laser laser Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
142 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 Fudan, December 24, / 70
143 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 1 P (1) Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
144 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 1 h P (1) radiation pressure noise Photons impart momentum to mirrors P h M 2 f 4 (2) Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
145 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 1 h P (1) radiation pressure noise Photons impart momentum to mirrors P h M 2 f 4 (2) 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 Fudan, December 24, / 70
146 Interferometer sensitivity improvement with squeezing Projected advanced LIGO sensitivity F. Ya. Khalili Phys. Rev. D 81, (2010) Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
147 Squeezing and EIT filter ( V out 1 V out 2 ) ( A 2 = + A 2 A 2 A 2 + ) ( V in 1 V in 2 ) [ ( )] ( + 1 A A ) ϕ ± = 1 2 (Θ + ± Θ ) A ± = 1 2 (T + ± T ) a ω p ω d c b ω bc Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
148 Squeezing and EIT filter ( V out 1 V out 2 ) ( A 2 = + A 2 A 2 A 2 + ) ( V in 1 V in 2 ) [ ( )] ( + 1 A A ) ϕ ± = 1 2 (Θ + ± Θ ) A ± = 1 2 (T + ± T ) a ω p ω d c b ω bc Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
![Squeezing and EIT filter ( V out 1 V out 2 ) ( A 2 = + A 2 A 2 A 2 + ) ( V in 1 V in 2 ) [ ( )] ( + 1 A 2 + + A 2 1 1 ) ϕ ± = 1](/docs-images/94/121757228/images/149-0.jpg "2 (Θ + ± Θ ) A ± = 1 2 (T + ± T ) a ω p ω d c b ω bc Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, 2013 61 / 70")
149 Squeezing and EIT filter ( V out 1 V out 2 ) ( A 2 = + A 2 A 2 A 2 + ) ( V in 1 V in 2 ) [ ( )] ( + 1 A A ) ϕ ± = 1 2 (Θ + ± Θ ) A ± = 1 2 (T + ± T ) a ω p ω d c b ω bc Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
![Squeezing and EIT filter ( V out 1 V out 2 ) ( A 2 = + A 2 A 2 A 2 + ) ( V in 1 V in 2 ) [ ( )] ( + 1 A 2 + + A 2 1 1 ) ϕ ± = 1](/docs-images/94/121757228/images/150-0.jpg "2 (Θ + ± Θ ) A ± = 1 2 (T + ± T ) a ω p ω d c b ω bc Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, 2013 61 / 70")
150 Squeezing and EIT filter ( V out 1 V out 2 ) ( A 2 = + A 2 A 2 A 2 + ) ( V in 1 V in 2 ) [ ( )] ( + 1 A A ) ϕ ± = 1 2 (Θ + ± Θ ) A ± = 1 2 (T + ± T ) a ω p ω d c b ω bc Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
151 Squeezing and EIT filter setup Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
152 Squeezing and EIT filter setup Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
153 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 Fudan, December 24, / 70 Noise power (dbm) Noise power (dbm)
154 Wide EIT filter and squeezing a ωp Peak ω d transmission = 52% b ω bc c FWHM= 4MHz 10 Input anti-squeezed noise Noise power (db) (i) attenuated (iii) (v) (vi) (iv) (ii) Noise frequency (MHz) 2.0 Calculated anti-squeezed Measured anti-squeezed Measured squeezed noise Calculated squeezed noise Input squeezed noise Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
155 Narrow EIT filter and squeezing a ωp Peak ω d transmission = 50% b ω bc c FWHM= 2MHz 10 Input anti-squeezed noise Noise power (db) filtered (iii) (v) (vi) (iv) (ii) Noise frequency (MHz) (i) Calculated anti-squeezed Measured anti-squeezed Measured squeezed noise Calculated squeezed noise Input squeezed noise Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
156 Control off no EIT and no squeezing at the output a 1 Probe transparency dependence on its detuning. ωp c Transparency [Arb. Unit] Peak transmission = 0% b ω bc Probe detuning [Arb. Unit] 10 8 control off Noise (db) Frequency (MHz) Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
157 Squeezing angle rotation θ θ ( V out 1 V out 2 ) = Locked at 300kHz ( cos 2 ϕ + sin 2 ϕ + sin 2 ϕ + cos 2 ϕ + ) ( A 2 + A 2 A 2 A2 + ) ( V in 1 V in 2 Locked at 1200kHz ) [ ( )] ( + 1 A A2 1 ) Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
158 Potential squeezing improvement with coated cells Vacuum cell Coated cell Noise (db) Frequency (MHz) Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
159 Potential squeezing improvement with coated cells Vacuum cell Coated cell 15 (a) antisqueezed 0.5 Noise power (db) 10 5 (b) squeezed Magnetic field (G) Noise level (db) Magnetic field (Arb. Units) Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
160 Summary We demonstrate fully atomic squeezed enhanced magnetometer with sensitivity as low as 1 pt/ Hz First demonstration of superluminal squeezing propagation with v g m/s c/ or time advancement of 11 µs Control over spacial mode and spectral profile of squeezing But more importantly Squeezing is exciting many applications benefit from squeezing there is still a lot of interesting physics to do Support from Eugeniy E. Mikhailov (W&M) Squeezed light Fudan, December 24, / 70
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