Squeezed light for advanced gravitational wave detectors and beyond

E. Oelker; L. Barsotti; S. Dwyer; D. Sigg; N. Mavalvala

doi:10.1364/OE.22.021106

Optics Express
Vol. 22,
Issue 17,
pp. 21106-21121
(2014)
•https://doi.org/10.1364/OE.22.021106

Squeezed light for advanced gravitational wave detectors and beyond

E. Oelker, L. Barsotti, S. Dwyer, D. Sigg, and N. Mavalvala

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E. Oelker, L. Barsotti, S. Dwyer, D. Sigg, and N. Mavalvala, "Squeezed light for advanced gravitational wave detectors and beyond," Opt. Express 22, 21106-21121 (2014)

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Abstract

Recent experiments have demonstrated that squeezed vacuum states can be injected into gravitational wave detectors to improve their sensitivity at detection frequencies where they are quantum noise limited. Squeezed states could be employed in the next generation of more sensitive advanced detectors currently under construction, such as Advanced LIGO, to further push the limits of the observable gravitational wave Universe. To maximize the benefit from squeezing, environmentally induced disturbances such as back scattering and angular jitter need to be mitigated. We discuss the limitations of current squeezed vacuum sources in relation to the requirements imposed by future gravitational wave detectors, and show a design for squeezed light injection which overcomes these limitations.

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Fig. 1: Maximum level of “effective” squeezing measurable in an optical system in the presence of optical losses and squeezed quadrature fluctuations, obtained by optimizing the amount of input squeezing [13]. Squeezing levels relative to shot noise are expressed in decibels. The squeezed quadrature fluctuations are root mean squared (RMS) fluctuations about a mean quadrature angle chosen to maximize the level of squeezing.

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Fig. 2: Top: A typical set-up for squeezing injection in the first demonstrations of squeezing at GEO600 and LIGO, both using DC readout [36,37]. The shaded gray region corresponds to the detector vacuum envelope; the cyan circles represent seismically isolated tables. The squeezed light source is housed outside of vacuum. The OPO cavity is locked to the green pump light. The squeezed (dashed red) and control (orange) fields enter vacuum through a viewport and are injected into the interferometer through the Output Faraday Isolator. A Squeezing Injection Faraday Isolator is inserted between the squeezed light source and the Output Faraday to provide additional attenuation of backscattered light [11, 14]. A small pickoff beam is sampled prior to the output mode cleaner (OMC) to control the squeezed quadrature angle. The squeezed and interferometer fields are measured in transmission through the OMC to obtain the gravitational wave signal. Details of the control topologies adopted in first generation detectors can be found in [11, 12]. Bottom: Proposed design for future detectors. This design features an in-vacuum OPO. The remainder of the squeezed light source remains outside of vacuum. The coherent control error signal [8] is now derived in transmission through the OMC [33]. Details of this new control topology can be found in section 6.

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Fig. 3: Back scattered light noise projections for three different scenarios: OPO placed on an optics table on the ground, without seismic isolation (similar to the LIGO H1 squeezing demonstration setup [14]), OPO placed on an isolated platform enclosed in the main LIGO vacuum envelope [42]; OPO suspended on an isolated platform enclosed in the main LIGO vacuum envelope (a single stage 1 Hz suspension on an isolated platform is considered here). In the first two cases, 30 dB of isolation from spurious light reaching the OPO is also assumed. The requirement curve optimistically targets 10 dB of broadband squeezing.

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Tables (2)

Table 1: Expected sources of loss for squeezing injection in Advanced LIGO (left), compared to projected losses achievable in the near future after replacing lossy Faraday rotators and polarizers, implementing active mode matching control, and reducing losses in the OMC.

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Table 2: Coupling coefficients A_ij calculated using the parameters for the advanced LIGO OMC. This cavity has a finesse of 390, higher order mode spacing of 58 MHz, and a free spectral range of 264.8 MHz. The detuning of the control sidebands, Ω, is 15 MHz. A mode order of n corresponds to any mode TEM_ij with i + j = n.

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Equations (24)

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L ≃ {(\frac{{\tilde{θ}}_{x} ω_{0} π}{λ})}^{2} + {(\frac{\tilde{Δ} x}{ω_{0}})}^{2}

L ≃ 0.01 \times [{(\frac{0.3 {\tilde{θ}}_{x}}{100 μ rad})}^{2} + {(\frac{\tilde{Δ} x}{10 μ m})}^{2}] for ω_{0} = 100 μ m

L ≃ 0.01 \times [{(\frac{0.3 {\tilde{θ}}_{x}}{10 μ rad})}^{2} + {(\frac{\tilde{Δ} x}{100 μ m})}^{2}] for ω_{0} = 1 mm

\frac{d θ_{sqz}}{d δ L} = \frac{ω}{\bar{L}} (\frac{1}{γ_{b}^{tot}} + \frac{1}{γ_{a}^{tot} (1 + x^{2})}) .

Δ θ_{alignment} = \frac{\sum_{i j} ρ_{i j}^{clf} ρ_{i j}^{ifo} \sin ϕ_{i j}}{1 + \sum_{i j} ρ_{i j}^{clf} ρ_{i j}^{ifo} \cos ϕ_{i j}} \approx \sum_{i j} ρ_{i j}^{clf} ρ_{i j}^{ifo} \sin ϕ_{i j} .

δ θ_{sqz} (t) \approx \sum_{i j} {\bar{ρ}}_{i j}^{clf} δ ρ_{i j}^{ifo} (1 + {\bar{ϕ}}_{i j}) δ ϕ_{i j} (t)

\frac{{RIN}_{sc}}{{RIN}_{q n}} (f) = 4 π δ z_{sc} (f) \sqrt{\frac{η_{P D} P_{sc}}{λ h c}}

P_{sc} = P_{sc, inc} R_{OPO} η_{loss}

\frac{{RIN}_{sc}}{{RIN}_{q n}} (f) = 4 π δ z_{sc} (f) \sqrt{\frac{η_{P D} P_{sc}}{λ h c}} \leq \frac{10^{s / 20}}{10} .

δ ν = \frac{ν}{l} δ l ~ 1 \frac{Hz}{\sqrt{Hz}} at 100 Hz

Δ θ_{alignment}^{trans} \approx \sum_{i j} A_{i j} ρ_{i j}^{clf} ρ_{i j}^{ifo} \sin ϕ_{i j}

δ θ_{sqz}^{trans} (t) \approx \sum_{i j} A_{i j} {\bar{ρ}}_{i j}^{clf} δ ρ_{i j}^{ifo} (1 + {\bar{ϕ}}_{i j}) δ ϕ_{i j} (t)

θ_{sqz} = θ_{B} / 2 - ϕ^{ifo} = ϕ - ψ / 2

\begin{array}{l} I_{err} \propto a_{00}^{ifo} a_{00}^{+} cos (- ϕ + θ_{d m}) + a_{00}^{ifo} a_{00}^{-} cos (ϕ - ψ + θ_{d m}) \\ + \sum_{i j} a_{i j}^{ifo} [a_{i j}^{+} cos (- ϕ + ϕ_{i j}^{ifo} - ϕ_{i j}^{+} + θ_{d m}) + a_{i j}^{-} cos (ϕ - ψ + ϕ_{i j}^{-} - ϕ_{i j}^{ifo} + θ_{d m})] \end{array}

\begin{array}{l} I_{err} \propto cos (- ϕ + θ_{d m}) + α cos (ϕ - ψ + θ_{d m}) \\ + \sum_{i j} ρ_{i j}^{ifo} ρ_{i j}^{clf} [cos (- ϕ + ϕ_{i j} + θ_{d m}) + α cos (ϕ - ψ - ϕ_{i j} + θ_{d m})] \end{array}

ρ_{i j}^{ifo} = \frac{a_{i j}^{ifo}}{a_{00}^{ifo}} ρ_{i j}^{clf} = \frac{a_{i j}^{+}}{a_{00}^{+}} ϕ_{i j} = ϕ_{i j}^{ifo} - ϕ_{i j}^{clf}

α = \frac{a_{00}^{+}}{a_{00}^{-}} = \frac{a_{i j}^{-}}{a_{i j}^{+}}

I_{err} \propto - (1 - α) [sin (Δ ϕ) + \sum_{i j} ρ_{i j}^{ifo} ρ_{i j}^{clf} sin (Δ ϕ - ϕ_{i j})]

Δ ϕ = \frac{\sum_{i j} ρ_{i j}^{clf} ρ_{i j}^{ifo} \sin ϕ_{i j}}{1 + \sum_{i j} ρ_{i j}^{clf} ρ_{i j}^{ifo} \cos ϕ_{i j}} \approx \sum_{i j} ρ_{i j}^{clf} ρ_{i j}^{ifo} \sin ϕ_{i j}

\begin{array}{l} a_{00, tr}^{ifo} = T (0) a_{00}^{ifo} & a_{i j, tr}^{ifo} = T (Δ ω (i, j)) a_{i j}^{ifo} \\ a_{00, tr}^{+} = T (Ω) a_{00}^{+} & a_{i j, tr}^{+} = T (Ω + Δ ω (i, j)) a_{i j}^{+} \\ a_{00, tr}^{-} = T r (- Ω) a_{00}^{-} & a_{i j, tr}^{-} = T (- Ω + Δ ω (i, j)) a_{i j}^{-} \end{array}

\begin{array}{l} ϕ_{tr}^{ifo} = ϕ^{ifo} & ϕ_{tr}^{+} = ϕ^{+} - π / 2 & ϕ_{tr}^{-} = ϕ^{-} + π / 2 \\ ψ_{tr} = ψ - π & ϕ_{tr} = ϕ - π / 2 & θ_{sqz, tr} = θ_{sqz} \end{array}

θ_{i j, tr}^{ifo} = ϕ_{i j}^{ifo} - π / 2 ϕ_{i j, tr}^{+} = ϕ_{i j}^{+} - π / 2 ϕ_{i j, tr}^{-} = ϕ_{i j}^{-} - π / 2

\begin{array}{l} I_{err} \propto cos (- ϕ_{tr} + θ_{d m}) + α cos (ϕ_{tr} - ψ_{tr} + θ_{d m}) + \sum_{i j} \frac{T (Δ ω (i, j))}{T (Ω)} ρ_{i j}^{ifo} ρ_{i j}^{clf} \\ \times [cos (- ϕ_{tr} + ϕ_{i j} + θ_{d m}) T (Ω + Δ ω (i, j)) + α cos (ϕ_{tr} - ψ_{tr} - ϕ_{i j} + θ_{d m}) T (- Ω + Δ ω (i, j))] \end{array}

\begin{matrix} Δ ϕ \approx \sum_{i j} A_{i j} ρ_{i j}^{ifo} ρ_{i j}^{clf} sin (ϕ_{i j}) \\ A_{i j} = \frac{T (Δ ω (i, j))}{(1 - α) T (Ω)} [T (Ω + Δ ω (i, j)) - α T (- Ω + Δ ω (i, j))] \end{matrix}

Loss Source	Estimated	Projected

OPO	2%	2%
Squeezing injection optics	1%	1%
Squeezing injection Faraday	3% – 5%	0% – 2%
Output Faraday in Reverse	3% – 5%	1% – 2%
Mode matching (squeezed beam to interferometer)	4% – 6%	1% – 2%
Alignment fluctuations (squeezed beam to interferometer)	0% – 1%	0% – 1%

Total injection losses	10% – 18%	5 % – 9%

Output Faraday	3% – 5%	1% – 2%
OMC transmission	3% – 6%	1% – 2%
Mode matching (interferometer to OMC)	4% – 6%	2% – 3%
Photo-detector	1%	1%

Total readout losses	10% to 17%	5% – 9%

Total losses	20% – 32%	9% – 17%

mode order	1	2	3	4	5
A_ij	0.0012	0.00071	0.0011	0.0086	0.0080

mode order	6	7	8	9	10
A_ij	0.00086	0.00075	0.0020	0.11	0.0014

Loss Source	Estimated	Projected

OPO	2%	2%
Squeezing injection optics	1%	1%
Squeezing injection Faraday	3% – 5%	0% – 2%
Output Faraday in Reverse	3% – 5%	1% – 2%
Mode matching (squeezed beam to interferometer)	4% – 6%	1% – 2%
Alignment fluctuations (squeezed beam to interferometer)	0% – 1%	0% – 1%

Total injection losses	10% – 18%	5 % – 9%

Output Faraday	3% – 5%	1% – 2%
OMC transmission	3% – 6%	1% – 2%
Mode matching (interferometer to OMC)	4% – 6%	2% – 3%
Photo-detector	1%	1%

Total readout losses	10% to 17%	5% – 9%

Total losses	20% – 32%	9% – 17%

mode order	1	2	3	4	5
A_ij	0.0012	0.00071	0.0011	0.0086	0.0080

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