Quantum noise of a white-light cavity using a double-pumped gain medium

Abstract

Laser interferometric gravitational-wave detectors implement Fabry-Pérot cavities to increase their peak sensitivity. However, this is at the cost of reducing their detection bandwidth, which originates from the propagation phase delay of the light. The "white-light-cavity" idea, first proposed by Wicht et al. [Opt. Commun. 34, 431 (1997)], is to circumvent this limitation by introducing anomalous dispersion, using a double-pumped gain medium, to compensate for such a phase delay. In this article, starting from the Hamiltonian of the atom-light interaction, we apply an input-output formalism to evaluate the quantum noise of the system. We find that apart from the additional noise associated with the parametric amplification process noted by others, the stability condition for the entire system poses an additional constraint. By surveying the parameter regimes where the gain medium remains stable (not lasing) and stationary, we find that there is no net enhancement of the shot-noise-limited sensitivity. Therefore, other gain media or different parameter regimes should be explored for realizing the white-light cavity.

Beating the Standard Sensitivity-Bandwidth Limit of Cavity-Enhanced Interferometers with Internal Squeezed-Light Generation

“…All of them can be seen as concepts of beating the standard sensitivitybandwidth limit. Two of these concepts: "white-light cavity" and "external squeezing," have been investigated intensively in recent years for the improvement of gravitational-wave detectors [20,22,36]. In this work, the third concept, "internal squeezing," is investigated, theoretically as well as experimentally and, also, in view of improving gravitational-wave detectors.…”

“…It broadens the cavity resonance without changing the finesse, in which case the uncertainty of the amplitude quadrature must increase above the vacuum level. Recently, it was proposed that the white-light cavity effect can be achieved by using an anomalously dispersive medium inside the interferometer [13][14][15][16][17][18][19][20][21][22].…”

Enhancing the Bandwidth of Gravitational-Wave Detectors with Unstable Optomechanical Filters

“…They generally fall into two categories: (i) a sensitivity-oriented category-using external squeezing [9,10] or internal squeezing [11,12] to reduce the shot noise while keeping broad bandwidth (external squeezing has been implemented in large-scale GW detectors [13,14] and is also planned for future upgrades [15][16][17]), and (ii) a bandwidth-oriented category-the so-called white-light-cavity idea [18][19][20][21][22][23][24][25]that uses an atomic medium with negative dispersion to cancel the positive dispersion of optical cavities.…”

Linear negative dispersion with a gain doublet via optomechanical interactions

“…Our result shows the potential possibility of using such optomechanical systems to build white-light signal recycling cavities in laser interferometric GW detectors for improving the sensitivity subject to the significant reduction of the mechanical resonator's thermal noise. Such a freespace optomechanical filter can be an alternative but less lossy compared to atomic systems where the light has to go through the medium [16][17][18][19]. Our demonstration shows the feasibility of using optomechanical interactions to achieve a required optical response.…”

“…In 2007, Salit and Shahriar [15] proposed a practical design for a white-light signal recycling GW interferometer by putting a negative dispersion medium inside the recycling cavity. By taking into account the quantum noise and stability of the system, Ma et al [16] excluded the possibility of using such a double-pumped optomechanical filter for improving the shot-noise-limited sensitivity of GW detectors in the stable regime. In order to achieve sensitivity improvement, one approach is exploring the unstable regime with additional feedback control for stabilization, as proposed by Miao et al [17].…”