The relative phase change between two light fields can be used as a fundamental parameter to measure the physical quantity causing this change. Therefore, amplifying the relative phase change becomes attractive to improve the measurement resolution. Phase amplification using a many-body entangled state (NOON state) is a well-known method; nevertheless, the preparation process for a high-number NOON state is difficult and sensitive to optical loss. Here, we propose and experimentally verify a concise phase amplification method with a tolerance of about five orders of magnitude for optical loss. The method is based on the optical-feedback-induced intracavity harmonics generation effect to amplify the phase change by 11 times, which is comparable to the highest level of about 10 experimentally reached in NOON states. Furthermore, the 20th intracavity harmonic is generated when the reinjected photon number increases, indicating that 20 times phase amplification is attainable. The proposed method has a prospect for precision measurement applications.
The relative phase change between two light fields can be used as a fundamental parameter to measure the physical quantity causing this change. Therefore, amplifying the relative phase change becomes attractive to improve the measurement resolution. Phase amplification using a many-body entangled state (NOON state) is a well-known method; nevertheless, the preparation process for a high-number NOON state is difficult and sensitive to optical loss. Here, we propose and experimentally verify a concise phase amplification method with a tolerance of about five orders of magnitude for optical loss. The method is based on the optical-feedback-induced intracavity harmonics generation effect to amplify the phase change by 11 times, which is comparable to the highest level of about 10 experimentally reached in NOON states. Furthermore, the 20th intracavity harmonic is generated when the reinjected photon number increases, indicating that 20 times phase amplification is attainable. The proposed method has a prospect for precision measurement applications.
The change in the relative phase between two light fields serves as a basic principle for the measurement of the physical quantity that guides this change. It would therefore be highly advantageous if the relative phase could be amplified to enhance the measurement resolution. One well-known method for phase amplification involves the use of the multi-photon number and path-entangled state known as the NOON state; however, a high-number NOON state is very difficult to prepare and is highly sensitive to optical losses. Here we propose and experimentally demonstrate in principle a phase amplifier scheme with the assistance of a harmonic generation process. The relative phase difference between two polarization modes in a polarized interferometer is amplified coherently four times with cascaded second-harmonic generation processes. We demonstrate that these amplification processes can be recycled and therefore have the potential to realize much higher numbers of multiple amplification steps. The phase amplification method presented here shows considerable advantages over the method based on NOON states and will be highly promising for use in precision optical measurements.
The presence of loss limits the precision of an approach to phase measurement using maximally entangled states, also referred to as NOON states. A calculation using a simple beam-splitter model of loss shows that, for all nonzero values L of the loss, phase measurement precision degrades with increasing number N of entangled photons for N sufficiently large. For L above a critical value of approximately 0.785, phase measurement precision degrades with increasing N for all values of N. For L near zero, phase measurement precision improves with increasing N down to a limiting precision of approximately 1.018Lradians, attained at N approximately equal to 2.218∕L, and degrades as N increases beyond this value. Phase measurement precision with multiple measurements and a fixed total number of photons NT is also examined. For L above a critical value of approximately 0.586, the ratio of phase measurement precision attainable with NOON states to that attainable by conventional methods using unentangled coherent states degrades with increasing N, the number of entangled photons employed in a single measurement, for all values of N. For L near zero this ratio is optimized by using approximately N=1.279∕L entangled photons in each measurement, yielding a precision of approximately 1.340L∕NTradians.
Optical interferometers, as precision measurement tools, inevitably experience optical path losses in practical applications, which introduce unavoidable vacuum noise and reduce the sensitivity in the phase estimation. To mitigate the effects of losses on sensitivity, we propose an enhanced interferometer scheme that integrates a Raman amplifier. This amplifier is strategically positioned within the lossy interference arm to counteract the reduction in phase sensitivity caused by losses. Our research highlights the crucial role of amplifier positioning, revealing that pre-amplification (PRA, placing the amplifier before the lossy section) significantly outperforms post-amplification (POA, placing the amplifier after the lossy section). PRA effectively enhances sensitivity by increasing the number of phase-sensitive particles and minimizing noise amplification. As the loss increases, the superiority of PRA in mitigating loss effects becomes increasingly evident. To validate our approach, we conducted experimental demonstrations. When the losses reach 90%, PRA experimentally achieves a sensitivity improvement of 4.6 dB compared with the case of only loss without the amplifier, equivalent to increasing the input laser power by over 8 times. PRA can effectively improve the robustness against losses for the practical application solely through the use of a coherent amplifier, with a simple technical implementation yet remarkable enhancement effects. We believe that current PRA-enhanced interferometry facilitates the practical implementation of phase measurement in environments characterized by significant loss.
Precise measurement is at the heart of physical science, and taking advantage of quantum effects, where practicable, affords sensitivity beyond the reach of classical methods. Rather than increasing photon number to reduce the de Broglie wavelength and achieve superresolution via quantum optics, the authors use quantum frequency up-conversion to realize 525-nm maximally entangled photons. This two-photon NOON state offers a visibility better than the threshold for beating the standard quantum limit, and could be used for high-precision metrology in many applications.
The presence of loss limits the precision of an approach to phase measurement using NOON states. A calculation using a simple beam-splitter model of loss shows that, for all nonzero values L of the loss, phase measurement precision degrades with increasing number N of entangled photons for N sufficiently large. For L above a critical value of approximately 0.785, phase measurement precision degrades with increasing N for all values of N. For L near zero, phase measurement precision improves with increasing N down to a limiting precision of approximately 1.018L radians, attained at N approximately equal to 2.218/L, and degrades as N increases beyond this value. Phase measurement precision with multiple measurements and a fixed total number of photons NT is optimized, for L near zero, by using approximately 1.279/L entangled photons in each measurement, yielding a precision of approximately 1.340 √ L/NT radians. 1 NOON States and the Heisenberg Limit The use of NOON states has been proposed as a means of performing phase measurements with a precision δφmin at the Heisenberg limit. In this limit, δφmin scales as δφmin ∼ 1/N, (1) This work was sponsored by the Air Force under Air Force Contract FA8721-05-C-0002. Opinions, interpretations, conclusions, and recommendations are those of the authors and are not necessarily endorsed by the U.S. Government. 1 with increasing photon number N, rather than at the standard quantum limit This fact can be seen as follows: NOON states are entangled states of the form
High precision interferometers are the building blocks of precision metrology and the ultimate interferometric sensitivity is limited by the quantum noise. Here, we propose and experimentally demonstrate a compact quantum interferometer involving two optical parametric amplifiers and the squeezed states generated within the interferometer are directly used for the phase-sensing quantum state. By both squeezing shot noise and amplifying phase-sensing intensity the sensitivity improvement of 4.86±0.24 dB beyond the standard quantum limit is deterministically realized and a minimum detectable phase smaller than that of all present interferometers under the same phase-sensing intensity is achieved. This interferometric system has significantly potential applications in a variety of measurements for tiny variances of physical quantities.