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arXiv:1101.1464 · Physical Review A

Precision frequency measurements with interferometric weak values

David J. Starling, P. Ben Dixon, Andrew N. Jordan, John C. Howell

Published Dec 20, 2010• 200 citations
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Abstract

We demonstrate an experiment which utilizes a Sagnac interferometer to measure a change in optical frequency of 129 $\ifmmode\pm\else\textpm\fi{}$ 7 $\text{kHz}/\sqrt{\text{Hz}}$ with only 2 mW of continuous-wave, single-mode input power. We describe the measurement of a weak value and show how even higher-frequency sensitivities may be obtained over a bandwidth of several nanometers. This technique has many possible applications, such as precision relative frequency measurements and laser locking without the use of atomic lines.

DOI
10.1103/physreva.82.063822

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We demonstrate an experiment which utilizes a Sagnac interferometer to measure a change in optical frequency of 129 \ifmmode±\else\textpm\fi\ifmmode\pm\else\textpm\fi{}\ifmmode±\else\textpm\fi 7 kHz/Hz\text{kHz}/\sqrt{\text{Hz}}kHz/Hz​ with only 2 mW of continuous-wave, single-mode input power. We describe the measurement of a weak value and show how even higher-frequency sensitivities may be obtained over a bandwidth of several nanometers. This technique has many possible applications, such as precision relative frequency measurements and laser locking without the use of atomic lines.
Weak measurement (WM) with state pre- and post-selection can amplify otherwise undetectable small signals and thus promise great potentials in precision measurements. Although frequency measurements offer the hitherto highest precision owing to stable narrow atomic transitions, it remains a long-standing interest to develop new schemes to further escalate their performance. Here, we propose and demonstrate a WM-enhanced spectroscopy technique which is capable of narrowing the resonance to 0.1 Hz in a room-temperature atomic vapor cell. Potential of this technique for precision measurement is demonstrated through weak magnetic field sensing. By judiciously pre- and post-selecting frequency-modulated input and output optical states in a nearly-orthogonal manner, a sensitivity of 7 fT/Hz\text{7 fT/}\sqrt{\text{Hz}}7 fT/Hz​ near DC is achieved, using only one laser beam of $\text{7 }\text{\mu W}$ power. Additionally, our results extend the WM framework to a non-Hermitian Hamiltonian, and shed new light in metrology and bio-magnetic field sensing applications.
We report on the use of an interferometric weak value technique to amplify very small transverse deflections of an optical beam. By entangling the beam's transverse degrees of freedom with the which-path states of a Sagnac interferometer, it is possible to realize an optical amplifier for polarization independent deflections. The theory for the interferometric weak value amplification method is presented along with the experimental results, which are in good agreement. Of particular interest, we measured the angular deflection of a mirror down to 400+/-200 frad and the linear travel of a piezo actuator down to 14+/-7 fm.
Optical interferometry plays an essential role in precision metrology such as in gravitational wave detection, gyroscopes, and environmental sensing. Weak value amplification enables reaching the shot-noise-limit of sensitivity, which is difficult for most optical sensors, by amplifying the interferometric signal without amplifying certain technical noises. We implement a generalized form of weak value amplification on an integrated photonic platform with a multi-mode interferometer. Our results pave the way for a more sensitive, robust, and compact platform for measuring phase, which can be adapted to fields such as coherent communications and the quantum domain. In this work, we show a 7 dB signal enhancement in our weak value device over a standard Mach-Zehnder interferometer with equal detected optical power, as well as frequency measurements with 2 kHz sensitivity by adding a ring resonator.
Abstract Weak measurement (WM) with state pre- and post-selection can amplify otherwise undetectable small signals and thus has potential in precision measurement applications. Although frequency measurements offer the hitherto highest precision due to the stable narrow atomic transitions, it remains a long-standing interest to develop new schemes to further escalate their performance. Here, we demonstrate a WM-enhanced correlation spectroscopy technique capable of narrowing the resonance linewidth down to 0.1 Hz in a room-temperature atomic vapour cell. The potential of this technique for precision measurement is demonstrated through weak magnetic-field sensing. By judiciously pre- and post-selecting frequency-modulated input and output optical states in a nearly orthogonal manner, a sensitivity of 7 fT Hz−1/2 at a low frequency near DC is achieved using only one laser beam with 15 µW of power. Additionally, our results extend the WM framework to a non-Hermitian Hamiltonian and shed new light on metrology and bio-magnetic field sensing.
A rotation-rate sensor was developed using atom interferometry and the Sagnac effect for matter waves. This device has a short-term sensitivity of 6× 10−10 rad/sec for a 1 second integration time, which is the best publicly reported value to date. It has high intrinsic accuracy because it relies on interactions between atoms and laser light that is stabilized to an atomic transition. Long-term stability is promising and characterization is currently underway. Potential applications include inertial navigation, geophysical studies, and general relativity tests such as verification of the Lense-Thirring and geodetic effects. The principle of operation is as follows: A thermal cesium atomic beam crosses three laser interaction regions where two-photon stimulated Raman transitions between cesium ground states transfer momentum to atoms and divide, deflect, and recombine the atomic wavepackets. Rotation induces a phase shift between the two possible trajectories and causes a change in the detected number of atoms with a particular internal state. Counterpropagating atomic beams form two interferometers using shared lasers for common-mode rejection, and the rotation phase shifts have opposite sign since the phase shift is proportional to the vector velocity of the atoms. Therefore, subtracting or adding the interferometer signals discriminates between rotation and transverse acceleration summed with laser arbitrary phase. Furthermore, in the inertial reference frame of the atoms, rotations Doppler-shift the Raman lasers. Adding Raman frequency shifts to cancel these Doppler-shifts allows operation at an effective zero rotation rate, improving sensitivity and bandwidth. Modulating these frequency shifts facilitates sensitive lock-in detection readout techniques.
In a passively mode-locked femtosecond ring dye laser the two counterpropagating pulses have a relative frequency difference Av that can be adjusted from a few hertz to megahertz by rotation of the cavity. These opposing pairs of pulses can thus be used to establish coherence between sublevels of a A transition in a resonant vapor. Sagnac spectroscopy is the distortion of the (previously linear) Sagnac response of the laser when such an atomic vapor (Sm) is inserted in the cavity. Even though the bandwidth of this unstabilized laser is of the order of 1013 Hz, spectroscopic measurements can be performed with 10 Hz accuracy. Applications include magnetic field measurement, lasing without inversion, and giant index of refraction.