Paired carriers as a way to reduce quantum noise of multicarrier gravitational-wave detectors

We explore new regimes of laser interferometric gravitational-wave detectors with multiple optical carriers which allow us to reduce the quantum noise of these detectors. In particular, we show that using two carriers with the opposite detunings, homodyne angles, and squeezing angles, but identical other parameters (the antisymmetric carriers), one can suppress the quantum noise in such a way that its spectrum follows the Standard Quantum Limit (SQL) at low frequencies. Relaxing this antisymmetry condition, it is also possible to slightly overcome the SQL in broadband. Combining several such pairs in the xylophone configuration, it is possible to shape the quantum noise spectrum flexibly.

Figure 1

Scheme of a second-generation laser GW detector with two carriers.

Figure 2

Plots of the total noise spectral densities of the baseline interferometer (7) at $\gamma =2\pi \times 500{\mathrm{s}}^{-1}$ (dots); the Sagnac speedmeter without the quantum noises cross-correlation (14) at $\gamma =2^{2/3}\times 2\pi \times 100{\mathrm{s}}^{-1}$ (solid); the Sagnac speedmeter with the cross-correlation (16) at $\gamma =2\pi \times 100{\mathrm{s}}^{-1}$, $\cot \zeta =4$ (dashes). Thin solid line: the SQL (4). In all cases, $J=(2\pi \times 100{)}^3{\mathrm{s}}^{-3}$ and $\eta =1$ (no losses).

Figure 3

Plots of the total quantum noise spectral density in the double antisymmetric carriers regime without squeezing (dashes), with 6 db squeezing (solid), and with 12 db squeezing (dash-dots). The parameters $\mathit{\Gamma }$, $\zeta$, $\beta$, and $\theta$ are given by Eqs. (c2) and (b5) and Table 3, respectively. Dots: the baseline interferometer (7), at $\gamma =2\pi \times 500{\mathrm{s}}^{-1}$ (dots). Thin solid line: the SQL (4). In all cases, $J=(2\pi \times 100{)}^3{\mathrm{s}}^{-3}$ and $\eta =1$ (no losses).

Figure 4

Plots of the total quantum noise spectral densities of the xylophone configuration with two pairs of antisymmetric carriers with 6 db (solid) and with 12 db (dash-dots) squeezing. The values of $\mathit{\Gamma }$ are given by Eq. (c2) for the lows-frequency pair and Eq. (c8) with ${\mathrm{\Omega }}_0=2\pi \times 600\mathrm{Hz}$ for the high-frequency pair. The parameters $\zeta$, $\beta$, and $\theta$ are given by Eq. (b5) and Table 3, respectively. The optical power is distributed evenly between all carriers. Dashes: the total quantum noise spectral densities of the individual pairs (in the absence of the other ones). Dots: the baseline interferometer (7), at $\gamma =2\pi \times 500{\mathrm{s}}^{-1}$. Thin solid line: the SQL (4). In all cases, the total circulating optical power corresponds to $J=(2\pi \times 100{)}^3{\mathrm{s}}^{-3}$ and $\eta =1$ (no losses).

Figure 5

Solid: plot of the total quantum noise spectral densities of the xylophone configuration with two broadband pairs of antisymmetric carriers, with the parameters defined in the same way as in Fig. 4, and one additional narrow-band pair with $\mathit{\Gamma }=4\pi \times 532.7{\mathrm{s}}^{-1}$ (the double frequency of the pulsar J0034-0534), $\beta =\pi /2-0.002$, $\theta =\pi /2$. The optical power is distributed among all carriers as 45%:45%:10%, and 6 db squeezing is used for all carriers. Dashes: the total quantum noise spectral densities of the individual pairs (in the absence of the other ones). Dots: the baseline interferometer (7), at $\gamma =2\pi \times 500{\mathrm{s}}^{-1}$. Thin solid line: the SQL (4). In all cases, the total circulating optical power corresponds to $J=(2\pi \times 100{)}^3{\mathrm{s}}^{-3}$ and $\eta =1$ (no losses).

Figure 6

Numerically optimized quantum noise spectral densities for one (top) and two (bottom) pairs of carriers, with $\eta =1$ (thick solid lines) and $\eta =0.95$ (thick dashed lines). The corresponding optimal parameters are listed in Table 2. In all cases, the total circulating optical power corresponds to $J=(2\pi \times 100{)}^3{\mathrm{s}}^{-3}$ and 6 db squeezing is used for all carriers. Dots: the baseline interferometer (7), at $\gamma =2\pi \times 500{\mathrm{s}}^{-1}$ (dots). Thin solid line: the SQL (4). Thin dashed line: the total classical instrumental noise.