Physics
Quantum mechanically, an object can be described by a pair of noncommuting observables, typically by its position and momentum. The precision to which these observables can be measured is limited by unavoidable quantum fluctuations. However, the method of “squeezing” allows the fluctuations to be manipulated, while preserving the Heisenberg uncertainty relation. This allows improved measurement precision for one observable at the expense of increased fluctuations in the other. Burd et al. now show that an additional displacement of a trapped atom results in amplification of the squeezing and a further improvement in the precision with which the displacement can be determined (see the Perspective by Schleier-Smith). This technique should be useful for a number of applications in metrology.
Science , this issue p. [1163][1]; see also p. [1137][2]
[1]: /lookup/doi/10.1126/science.aaw2884
[2]: /lookup/doi/10.1126/science.aax0143
Physics
Quantum mechanically, an object can be described by a pair of noncommuting observables, typically by its position and momentum. The precision to which these observables can be measured is limited by unavoidable quantum fluctuations. However, the method of “squeezing” allows the fluctuations to be manipulated, while preserving the Heisenberg uncertainty relation. This allows improved measurement precision for one observable at the expense of increased fluctuations in the other. Burd et al. now show that an additional displacement of a trapped atom results in amplification of the squeezing and a further improvement in the precision with which the displacement can be determined (see the Perspective by Schleier-Smith). This technique should be useful for a number of applications in metrology.
Detection of the weakest forces in nature is aided by increasingly sensitive measurements of the motion of mechanical oscillators. However, the attainable knowledge of an oscillator's motion is limited by quantum fluctuations that exist even if the oscillator is in its lowest possible energy state. We demonstrate a technique for amplifying coherent displacements of a mechanical oscillator with initial magnitudes well below these zero-point fluctuations. When applying two orthogonal squeezing interactions, one before and one after a small displacement, the displacement is amplified, ideally with no added quantum noise. We implemented this protocol with a trapped-ion mechanical oscillator and determined an increase by a factor of up to 7.3 (±0.3) in sensitivity to small displacements.
We present a unified framework, based on quantum metrology concepts, for defining and quantifying deterministic noiseless quantum amplification of parameter-dependent processes, which plays an important role in increasing the precision of quantum sensing.Recent experiments [Burd et al., Science 364, 1163 (2019)] can be encompassed by this concept, which also leads to new suggestions of experimental work.The unified view presented here allows the identification of the basic steps for quantum amplification and of the measurements that lead to the best possible precision, beyond the quantum standard limit, in the estimation of parameters involved in the process.This is applied to the estimation of displacements of trapped ions and of the phase in SU(1,1) optical interferometers and atomic interferometry.
Weak measurements have been under intensive investigation in both experiment and theory. Numerous experiments have indicated that the amplified meter shift is produced by the post-selection, yielding an improved precision compared to conventional methods. However, this amplification effect comes at the cost of a reduced rate of acquiring data, which leads to an increasing uncertainty to determine the level of meter shift. From this point of view, a number of theoretical works have suggested that weak measurements cannot improve the precision, or even damage the metrology information due to the post-selection. In this review, we give a comprehensive analysis of the weak measurements to justify their positive effect on prompting measurement precision. As a further step, we introduce two modified weak measurement protocols to boost the precision beyond the standard quantum limit. Compared to previous works beating the standard quantum limit, these protocols are free of using entangled or squeezed states. The achieved precision outperforms that of the conventional method by two orders of magnitude and attains a practical Heisenberg scaling up to n=106 photons.
Quantum Physics
Exploiting the quantum-mechanical properties of quantum systems offer the possibility of developing devices for enhanced precision measurement and sensing applications. These devices have, however, required low-noise detection capabilities that have hampered their development. Hosten et al. describe a method that manipulates a coherent cloud of cold rubidium atoms in a way that relaxes the ultrasensitive detection requirements. The general method may be applied to other coherent quantum systems.
Science , this issue p. [1552][1]
[1]: /lookup/doi/10.1126/science.aaf3397
Quantum Sensors, like atom interferometers (AI), can be employed for high-precision measurements of inertial forces, including their application as gravimeters, gradiometers, accelerometers, and gyroscopes. Their measurement principle relies on ultracold atoms that are prepared in quantum-mechanical superposition states in external degrees of freedom. These states can be prepared by a momentum transfer of a Raman laser. Then the superposition state senses the effect of an inertial force, which induce a corresponding relative phase. The phase is read out by a final coupling which converts the interferometric phase into a atom number difference between the two states. The difference provides an estimate of the interferometric phase and the corresponding quantity of interest. The quantum mechanical noise of the atomic ensemble cause a fundamental uncertainty of this estimation, which I analyze for generic AIs. For small atomic densities, the quantum phase noise of the ensemble limits the interferometric sensitivity. For large densities, quantum number fluctuations generate density fluctuations, which generates phase noise. I show that these two competing effects result in an optimal atom number with a maximal interferometer resolution. Squeezed atomic samples allow for a reduction of the quantum noise of one quantity at the expense of an increased noise along of a conjugate quantity. Phase and number are such quantities which obey to a variant of Heisenberg’s uncertainty principle. Neither phase nor number squeezing can improve the maximal interferometer resolution. As one main result of this thesis, I show how an optimal squeezing in between number and phase squeezing, allows for a fundamental improvement. I evaluate possible experimental paths to implement the proposed protocol. Concepts for a squeezing-enhanced operation of external-degree AIs have not yet been demonstrated. I propose and implement an atomic gravimeter, which is designed to accept spin-squeezed atomic states as input states. The interferometer is designed such that the interferometer couplings are performed in spin space, while the phase accumulation is performed in momentum states. For this interferometer, the squeezed input can be directly obtained from spin dynamics in spinor Bose-Einstein condensates. The main noise contributions in the experiment are analyzed, which results in a factor of 84 above the relevant quantum limit, preventing a squeezing enhancement so far. I outline a suppression of the main noise source, uncontrolled AC Stark shift on the squeezed mode and propose future important applications, including test of spontaneous collapse theories and an improvement of large-scale, high-precision gradiometers.
According to the Heisenberg uncertainty principle, the precision of any physical quantity measurement is limited by quantum fluctuation in general, which leads to the so-called standard quantum limit (SQL). The SQL can be beaten by using squeezed light, hence enhancing the measurement accuracy. Squeezed light is a typical nonclassical light, it exhibits reduced noise in one quadrature component. Since Caves proposed the scheme of phase measurement enhancement with squeezing, squeezed light has been used to enhance measurement precision in many areas. This review focuses on the following four kinds of precision measurements based on squeezed light: the measurements of relative phase, small lateral displacement and tilt, magnetic field, and clock synchronization. For all of these measurements, vacuum squeezing has been used to enhance measurement precision, while the types of squeezing (squeezing angle, transverse mode, polarization etc.) are different. For phase measurement, quadrature squeezing is injected into the conventionally unused input port of Mach-Zehnder interferometer (MZI) or Michelson interferometer (MI). For displacement or tilt measurement, a vacuum squeezing beam of a special transverse mode is coupled into an intense coherent beam, yielding a spatial-squeezed light whose transverse position or tilt angle noise is lower than that of a classical light beam. Based on the Faraday effect of polarization rotation, the magnetic field can be detected precisely. The precision can be increased further by using the polarization squeezing. The polarization squeezing can be generated by coupling two orthogonal polarized beams together, a coherent beam and a vacuum squeezed beam. Various polarization squeezing can be illustrated on the Poincaré sphere. Finally, in the clock synchronization based on the optical frequency comb, squeezed light can be used to enhance the time measurement precision. A theoretical scheme with multimode squeezing of supermode (a kind of mode describing the frequency mode of a pulse laser beam) is introduced. The squeezing has extensively been applied into the quantum precision measurements such as gravitational wave detection as well as biological measurement and will play a more important role in the near future.