Nano-Kelvin Thermometry and Temperature Control: Beyond the Thermal Noise Limit

Abstract

We demonstrate thermometry with a resolution of 80 nK= ffiffiffiffiffiffi Hz p using an isotropic crystalline whispering-gallery mode resonator based on a dichroic dual-mode technique. We simultaneously excite two modes that have a mode frequency ratio that is very close to two (AE0.3 ppm). The wavelength and temperature dependence of the refractive index means that the frequency difference between these modes is an ultrasensitive proxy of the resonator temperature. This approach to temperature sensing automatically suppresses sensitivity to thermal expansion and vibrationally induced changes of the resonator. We also demonstrate active suppression of temperature fluctuations in the resonator by controlling the intensity of the driving laser. The residual temperature fluctuations are shown to be below the limits set by fundamental thermodynamic fluctuations of the resonator material. DOI: 10.1103/PhysRevLett.112.160801 PACS numbers: 07.20.Dt, 42.60.Da, 42.62.Fi The high-resolution measurement of energy has long fascinated humans with its culmination seen in ultra-highsensitivity calorimeters [1,2] and bolometers [3]. These and related ideas have found a broad range of applications, including bolometric superconducting photon counters for quantum communication [4] and ultrasensitive radio astronomy [5,6]. The record for absolute thermometric sensitivity has been realized at cryogenic temperatures, achieving better than 100 pK= ffiffiffiffiffiffi Hz p [7]. In this Letter, we develop a new method to measure temperature based on excitation of two well-separated modes in a millimeter-scale whispering-gallery (WG) optical resonator. WG mode resonators have exceptionally high Q factors and can provide the potential of providing high-stability microwave and optical signals [8][9][10][11][12]. Recently, they have been applied to high-sensitivity label-free sensors for molecules and viruses [13,14] and for optical comb generation [15]. Nonetheless, an issue that afflicts all of these applications is the high temperature sensitivity of WG resonators [12,16], particularly when compared to conventional vacuum-spaced Fabry-Perot resonators [17][18][19][20][21]. In this Letter, we turn this problem to our advantage by using the WG resonator as an ultrasensitive thermometer.To suppress unwanted temperature fluctuations in WG resonators, several groups have demonstrated in situ thermometry by measuring the frequency difference between two orthogonally polarized modes. The best of these techniques have demonstrated a resolution of ∼100 nK= ffiffiffiffiffiffi Hz p [22], and subsequent temperature stabilization based on this sensing has resulted in improvement to the long-term frequency stability [23,24]. In contrast, we present a two-color approach to measure the resonator temperature with high resolution. In comparison to the birefringent dual-mode technique, our approach can be used in both anisotropic and isotropic resonators, which expands the range of material candidates. Isotropic materials have shown the highest Q facto...

Refractometry with Ultralow Detection Limit Using Anisotropic Whispering-Gallery-Mode Resonators

“…We expect the spectral signature of Γ 0 to be identical to the free-running temperature fluctuations f a , since the ambient fluctuations are mapped into P TM , through our temperature-control technique. Earlier measurements predict that this differential Kerr effect will only contribute for Fourier frequencies below 0.01 Hz [20].…”

“…Furthermore, f b is also sensitive to the resonator temperature because the thermooptic coefficient is wavelength dependent. This temperature dependence can be expressed as 1=f TM df b =dT ¼ 2ðβ 1064;e − β 532;e Þ ≡ β λ , where β 532;e is the thermo-optic coefficient at 532 nm for the extraordinary refractive index and we define β λ as the wavelength-dependent thermo-optic coefficient [20].…”

“…In calculating these Kerr shifts, care must be taken in accounting for different effective mode areas of the modes and the overlap with the total intensity distribution [20]. In our experimental situation, the intracavity power of the 1064-nm TM mode P TM is much higher than the other two modes and hence the overlap of this intensity distribution with the three modes determines the result, i.e., γ x ¼ P TM κ=n s R jM TM j 2 jM x j 2 dA, where x ¼ TE, TM, or G; κ is the Kerr coefficient for the material; and M x is the transverse mode amplitude normalized so that R jM x j 2 dA ¼ 1; and dA is an elemental area transverse to the mode propagation direction.…”

“…First, the frequency difference between two orthogonally polarized modes in the same mode family detects the resonator temperature [18][19][20]. In a second step, we stabilize the resonator temperature by adjusting the optical input power to the resonator so that this frequency difference is kept constant.…”

Taking detection to the limit with optical microcavities: Recent advances presented at the 560. WE Heraeus Seminar

“…WGMs enable real time detection of such interactions, with high sensitivity and time resolution [7][8][9][10][11][12][13]. However, the applications of WGMs as transducers are by far not only limited to biosensing but they can find broad applications as nanoparticle and virus analyzers [14][15][16][17], for measurements of the viscosity of a fluid [18], as refractive index sensors [19,20], monitors of unspecific protein adsorption, down to single proteins [21,22], as metal ion detectors [23], as thermometers [24], detectors of heavy water [25], for determining absolute absorption cross sections [26], tuning of WGMs on-chip [27,28], and for monitoring water adsorption [29,30], to name a few. Developing these varied applications provides a solid ground for improving this technology and cross-fertilizing its different implementations, which taken together have great importance in health care, environmental monitoring, and fundamental studies in the life sciences.…”