The quantum correlation of light and atomic collective excitation can be used to compose an SU(1,1)-type hybrid light-atom interferometer, where one arm in the optical SU(1,1) interferometer is replaced by the atomic collective excitation. The phase-sensing probes include not only the photon field but also the atomic collective excitation inside the interferometer. For a coherent squeezed state as the phase-sensing field, the phase sensitivity can approach the Heisenberg limit under the optimal conditions. We also study the effects of the loss of light field and the dephasing of atomic excitation on the phase sensitivity. This kind of active SU(1,1) interferometer can also be realized in other systems, such as circuit quantum electrodynamics in microwave systems, which provides a different method for basic measurement using the hybrid interferometers.
The quantum correlation of light and atomic collective excitation can be used to compose an SU(1,1)-type hybrid light-atom interferometer, where one arm in the optical SU(1,1) interferometer is replaced by the atomic collective excitation. The phase-sensing probes include not only the photon field but also the atomic collective excitation inside the interferometer. For a coherent squeezed state as the phase-sensing field, the phase sensitivity can approach the Heisenberg limit under the optimal conditions. We also study the effects of the loss of light field and the dephasing of atomic excitation on the phase sensitivity. This kind of active SU(1,1) interferometer can also be realized in other systems, such as circuit quantum electrodynamics in microwave systems, which provides a different method for basic measurement using the hybrid interferometers.
Collective atomic excitation can be realized by the Raman scattering. Such a photon-atom interface can form an SU(1,1)-typed atom-light hybrid interferometer, where the atomic Raman amplification processes take the place of the beam splitting elements in a traditional Mach-Zehnder interferometer. We numerically calculate the phase sensitivities and the signal-to-noise ratios (SNRs) of this interferometer with the method of homodyne detection and intensity detection, and give their differences of the optimal phase points to realize the best phase sensitivities and the maximal SNRs from these two detection methods. The difference of the effects of loss of light field and atomic decoherence on measure precision is analyzed.
A new type of hybrid atom-light interferometer is demonstrated with atomic Raman amplification processes replacing the beam splitting elements in a traditional interferometer. This nonconventional interferometer involves correlated optical and atomic waves in the two arms. The correlation between atoms and light developed with the Raman process makes this interferometer different from conventional interferometers with linear beam splitters. It is observed that the high-contrast interference fringes are sensitive to the optical phase via a path change as well as the atomic phase via a magnetic field change. This new atom-light correlated hybrid interferometer is a sensitive probe of the atomic internal state and should find wide applications in precision measurement and quantum control with atoms and photons.
Quantum-enhanced precision measurements have emerged as one of the most useful applications of quantum optics. Exploiting quantum states of light and quantum processes, classical measurement limits can be surpassed, leading to improvements in areas including clocks, spectroscopy, magnetometry, and imaging. One measurement where straightforward quantum enhancements are possible is phase sensing with an interferometer. One can inject squeezed vacuum states into the dark port of the beamsplitter in a traditional interferometer to reduce the quantum noise and reach phase sensitivities beyond the shot noise limit. An alternate approach is to replace the beamsplitters of an interferometer with nonlinear parametric amplifiers, which produce nonclassical states of light that can be used to surpass classical performance. This so called SU(1,1) interferometer can theoretically approach sensitivities that scale as 1/n, the Heisenberg limit where n is the interior phase sensing photon number, compared to the shot noise limit of 1/ √ n for a traditional interferometer [1]. I will present our group’s experimental progress in testing a Mach-Zender SU(1,1) interferometer using four-wave mixers (4WMs) in hot Rb atoms as the parametric beamsplitters. The 4WM process generates entangled twin beams which serve as the two arms of the interferometer, and are then recombined in a second 4WM cell, resulting in a phase-sensitive output. We will extend the work done on this interferometer [2, 3] by performing a detailed analysis of the output signal to noise through homodyne measurements, and will attempt to observe the better-than-shot-noise scaling of the sensitivity. We will also consider the various difficulties of this optical interferometer such as the susceptibility to loss and imperfect mode-matching within the interferometer. Our group is also considering an analogous SU(1,1) interferometer in a cold atom system. Collisions in a spinor Bose-Einstein condensate of sodium atoms give rise to a 4WM process that produces spin states of the atoms which are entangled in atom number. These interactions can be controlled to set up an SU(1,1) atom interferometer, where the relevant measurements are now atomic population differences rather than photon intensities. These enhancements can lead to drastic improvements in atomic spin interferometry [3, 4].
We theoretically investigate an interferometer composed of four four-wave-mixers by Lie group method. Lie group SU(1,2) characterizes the mode transformations of this kind of interferometer. With vacuum state inputs, the phase sensitivity of SU(1,2) interferometer achieves the Heisenberg limit, and the absolute accuracy beats SU(1,1) interferometer because of higher intensity of light inside the interferometer. For different input cases, the optimal combination of output photon number for detection to obtain the best phase sensitivity is calculated. Our research on SU(1,2) interferometer sheds light on the performance of SU(1,n) interferometer in quantum metrology.
The measurement of physical quantities and measurement units standard promote the development of metrology. Especially, the developments of laser interference and atomic frequency standard bring a revolutionary leap for metrology. Many precision measurement techniques have been proposed and experimentally demonstrated, such as gravitational wave measurements and laser gyroscopes based on laser interferometry, and atomic clocks and atomic gyroscopes based on the atom interferometry. Recently, a new branch of science, quantum metrology, has grown up to further explore and exploit the quantum techniques for precision measurement of physical quantities.#br#This paper will focus on recent developments in quantum metrology and interference based on coherence and correlation of light and atom. Firstly, we briefly review the development of metrology. Then, we introduce our own researches in recent years, including quantum-correlation SU(1,1) optical interferometer based on four wave mixing process in atomic vapor and the atom-light hybrid interferometer based on Raman scattering in atomic vapor.#br#Interferometer is a powerful tool to measure physical quantities sensitive to the inference wave with high precision, and has been widely used in scientific research, industry test, navigation and guidance system. For example, the laser interferometer is able to measure optical phase sensitive quantities, including length, angular velocity, gravitational wave and so on. Meanwhile, the atom interferometer is sensitive to the change of atomic phase caused by the light, gravity, electric and magnetic fields. As a new type of interferometry, the atom-light hybrid interferometer, is sensitive to both the optical phase and atomic phase. Furthermore, SU(1,1) interferometer and nonlinear atom-light hybrid interferometer have the ability to beat the standard quantum limit of phase sensitivity. Quantum interference technology, whose phase measurement accuracy can break through the limit of standard quantum limit, is the core of quantum metrology and quantum measurement technology.
We theoretically study the phase sensitivity of an SU(1,1) interferometer with a coherent state in one input port and a squeezed-vacuum state in the other input port using the method of homodyne detection. In this interferometer, beam splitting and recombination are generated by the parametric amplifiers instead of the beam splitters. Compared with the traditional Mach–Zehnder interferometer, the phase sensitivity of this interferometer can be improved due to the amplification process of the parametric amplifiers. Combined with the squeezed state input, the sensitivity can be improved further due to the noise reduction. The phase sensitivity of our scheme can approach the Heisenberg limit and the associated optimal condition is analyzed. The scheme can be implemented with current experimental technology.