Quantum optics and squeezed states of light
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1 Quantum optics and squeezed states of light Eugeniy E. Mikhailov The College of William & Mary June 15, 2012 Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
2 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) Quantum optics June 15, / 44
3 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) Quantum optics June 15, / 44
4 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
5 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
6 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
7 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
8 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
9 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
10 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
11 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
12 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
13 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
14 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
15 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
16 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
17 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
18 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
19 Classical field E() = a e i = a cos() + i a sin() = + i, = ωt kz 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
20 Classical quadratures vs time in a rotating frame E() = a e i = a cos() + i a sin() = + i, = ωt kz t Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
21 Reality check quadratures vs time E() = a e i = a cos() + i a sin() = + i, = ωt kz t Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
22 Detector quantum noise Simple photodetector N V V N V N Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
23 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) Quantum optics June 15, / 44
24 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) Quantum optics June 15, / 44
25 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) Quantum optics June 15, / 44
26 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) Quantum optics June 15, / 44
27 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) Quantum optics June 15, / 44
28 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) Quantum optics June 15, / 44
29 Coherent state is minimum uncertainty state = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
30 Coherent state is minimum uncertainty state = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
31 Coherent state is minimum uncertainty state = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
32 Coherent state is minimum uncertainty state = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
33 Coherent state is minimum uncertainty state = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
34 Coherent state is minimum uncertainty state = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
35 Coherent state is minimum uncertainty state = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
36 Coherent state is minimum uncertainty state = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
37 Coherent state is minimum uncertainty state = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
38 Coherent state is minimum uncertainty state = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
39 Coherent state is minimum uncertainty state = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
40 Coherent state is minimum uncertainty state = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
41 Coherent state is minimum uncertainty state = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
42 Coherent state is minimum uncertainty state = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
43 Coherent state is minimum uncertainty state = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
44 Coherent state is minimum uncertainty state = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
45 Amplitude squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
46 Amplitude squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
47 Amplitude squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
48 Amplitude squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
49 Amplitude squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
50 Amplitude squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
51 Amplitude squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
52 Amplitude squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
53 Amplitude squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
54 Amplitude squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
55 Amplitude squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
56 Amplitude squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
57 Amplitude squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
58 Amplitude squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
59 Amplitude squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
60 Amplitude squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
61 Phase squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
62 Phase squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
63 Phase squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
64 Phase squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
65 Phase squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
66 Phase squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
67 Phase squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
68 Phase squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
69 Phase squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
70 Phase squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
71 Phase squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
72 Phase squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
73 Phase squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
74 Phase squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
75 Phase squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
76 Phase squeezed states = 1/4 0 1/2π π 3/2π 2π Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
77 Squeezed quantum states zoo Unsqueezed coherent Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
78 Squeezed quantum states zoo Unsqueezed coherent Amplitude squeezed Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
79 Squeezed quantum states zoo Unsqueezed coherent Amplitude squeezed Phase squeezed Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
80 Squeezed quantum states zoo Unsqueezed coherent Amplitude squeezed θ Phase squeezed Vacuum squeezed θ Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
81 Possible squeezing applications improvements any shot noise limited optical sensors noiseless signal amplification secure communications (you would notice eavesdropper) 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) Quantum optics June 15, / 44
82 Squeezing and interferometer Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
83 Squeezing and interferometer Vacuum input laser Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
84 Squeezing and interferometer Vacuum input Squeezed input laser laser Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
85 Laser Interferometer Gravitational-wave Observatory L = 4 km h L m rad Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
86 Squeezing level vs time (unlocked) A quantum-enhanced prototype gravitational-wave detector, Nature Physics, 4, , (2008). Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
87 GW 40m detector and squeezer Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
88 GW 40m detector with 4dB of squeezed vacuum Signal to noise improvement by factor of 1.43 Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
89 Squeezed field generation recipe Take a vacuum state 0 > H = 1 2 Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
90 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) Quantum optics June 15, / 44
91 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) Quantum optics June 15, / 44
92 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) Quantum optics June 15, / 44
93 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) Quantum optics June 15, / 44
94 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) Quantum optics June 15, / 44
95 Tools for squeezing Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
96 Tools for squeezing Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
97 Tools for squeezing 2ω b b a ω ω Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
98 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) Quantum optics June 15, / 44
99 Squeezer appearance Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
100 Squeezer appearance Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
101 Squeezer appearance Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
102 Crystal squeezing setup scheme PZT LASER PM MC PM PZT SHG AM PM AOM Oscilloscope AM Spectrum Analyzer PM PM PM OPA Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
103 Cavity parameters with squeezing Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
104 Cavity parameters with squeezing Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
105 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) Quantum optics June 15, / 44
106 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) Quantum optics June 15, / 44
107 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) Quantum optics June 15, / 44
108 Quantum memory with atomic ensembles 1 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) Quantum optics June 15, / 44
109 Quantum memory with atomic ensembles Probe transparency dependence on its detuning. a Probe transparency dependence on its detuning. 1 1 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) Quantum optics June 15, / 44
110 Quantum memory with atomic ensembles Probe transparency dependence on its detuning. a Probe transparency dependence on its detuning. 1 1 Transparency [Arb. Unit] ω p ω d Transparency [Arb. Unit] Probe detuning [Arb. Unit] Storage and retrieval b ω bc c Probe detuning [Arb. Unit] Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
111 Quantum memory with atomic ensembles Probe transparency dependence on its detuning. a Probe transparency dependence on its detuning. 1 1 Transparency [Arb. Unit] ω p ω d Transparency [Arb. Unit] Probe detuning [Arb. Unit] Storage and retrieval single photon b ω bc c Probe detuning [Arb. Unit] Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
112 Quantum memory with atomic ensembles Probe transparency dependence on its detuning. a Probe transparency dependence on its detuning. 1 1 Transparency [Arb. Unit] ω p ω d Transparency [Arb. Unit] c Probe detuning [Arb. Unit] Probe detuning [Arb. Unit] b ω bc Storage and retrieval single photon squeezed state (Furusawa and Lvovsky PRL ) Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
113 Quantum memory with atomic ensembles Probe transparency dependence on its detuning. a Probe transparency dependence on its detuning. 1 1 Transparency [Arb. Unit] ω p ω d Transparency [Arb. Unit] c Probe detuning [Arb. Unit] Probe detuning [Arb. Unit] b ω bc Storage and retrieval single photon squeezed state (Furusawa and Lvovsky PRL ) Squeezed state requirements for a quantum memory probe Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
114 Quantum memory with atomic ensembles Probe transparency dependence on its detuning. a Probe transparency dependence on its detuning. 1 1 Transparency [Arb. Unit] ω p ω d Transparency [Arb. Unit] Probe detuning [Arb. Unit] Storage and retrieval single photon b squeezed state (Furusawa and Lvovsky PRL ) Squeezed state requirements for a quantum memory probe ω bc c Probe detuning [Arb. Unit] squeezing carrier at atomic wavelength (780nm, 795nm) squeezing within narrow resonance window at frequencies(<100khz) Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
115 Quantum memory with atomic ensembles Probe transparency dependence on its detuning. a Probe transparency dependence on its detuning. 1 1 Transparency [Arb. Unit] ω p ω d Transparency [Arb. Unit] Probe detuning [Arb. Unit] Storage and retrieval single photon b squeezed state (Furusawa and Lvovsky PRL ) Squeezed state requirements for a quantum memory probe ω bc c Probe detuning [Arb. Unit] squeezing carrier at atomic wavelength (780nm, 795nm) squeezing within narrow resonance window at frequencies(<100khz) Traditional nonlinear crystal based squeezers are capable of it, but they are extremely technically challenging especially at short wave length. Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
116 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) (1) Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
117 Setup V.Sq LO PBS 87 RB PBS Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
118 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) Quantum optics June 15, / 44
119 Optical magnetometer and non linear Faraday effect 87 Rb D 1 line F'=2 F'=1 m'=0 + - F=2 F=1 m=-1 m=0 m=1 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) Quantum optics June 15, / 44
120 Optical magnetometer and non linear Faraday effect 87 Rb D 1 line F'=2 F'=1 m'=0 + - F=2 F=1 m=-1 m=0 m=1 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) Quantum optics June 15, / 44
121 Magnetometer response vs atomic density Slope of rotation signal (V/µT) Normalized transmission Atomic density (atoms/cm 3 ) Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
122 Shot noise limit of the magnetometer 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) Quantum optics June 15, / 44
123 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) Quantum optics June 15, / 44
124 Magnetometer noise floor improvements Noise spectral density (dbm/hz) (b) (a) (b) (a) Noise Frequency (khz) Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
125 Magnetometer sensitivity vs atomic density Sensitivity pt/ Hz (a) (b) coherent probe squeezed probe Atomic density (atoms/cm 3 ) Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
126 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 MAGNETIC B Rb Cell Rb Cell 87 Rb SHIELDING SCOPE LENS BPD λ/2 PBS Noise power (db) (b) squeezed Magnetic field (G) Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
127 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) Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
128 Summary Squeezing is exiting Many applications benefit from squeezing interferometers gravitational antennas magnetometers quantum memory There is still a lot of interesting physics to do Eugeniy E. Mikhailov (W&M) Quantum optics June 15, / 44
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