We show the utility of the weak value amplification to observe the quantum interference between two close lying atomic coherent states in a post-selected atomic cat state, produced in a system of N identical two-level atoms weakly interacting with a single photon field. Through the observation of the negative parts of the Wigner distribution of the post-selected atomic cat state, we find that the post-selected atomic cat state becomes more nonclassical when the post-selected polarization state of the single photon field tends toward becoming orthogonal to its pre-selected state. We show that the small phase shift in the post-selected atomic cat state can be amplified via measuring the peak shift of its phase distribution when the post-selected state of the single photon field is nearly orthogonal to its pre-selected state. We find that the amplification factor of 15 [5] can be obtained for a sample of 10 [100] atoms. This effectively provides us with a method to discriminate between two close lying states on the Bloch sphere. We discuss possible experimental implementation of the scheme, and conclude with a discussion of the Fisher information.
We show the utility of the weak value amplification to observe the quantum interference between two close lying atomic coherent states in a post-selected atomic cat state, produced in a system of N identical two-level atoms weakly interacting with a single photon field. Through the observation of the negative parts of the Wigner distribution of the post-selected atomic cat state, we find that the post-selected atomic cat state becomes more nonclassical when the post-selected polarization state of the single photon field tends toward becoming orthogonal to its pre-selected state. We show that the small phase shift in the post-selected atomic cat state can be amplified via measuring the peak shift of its phase distribution when the post-selected state of the single photon field is nearly orthogonal to its pre-selected state. We find that the amplification factor of 15 [5] can be obtained for a sample of 10 [100] atoms. This effectively provides us with a method to discriminate between two close lying states on the Bloch sphere. We discuss possible experimental implementation of the scheme, and conclude with a discussion of the Fisher information.
Weak value amplification (WVA) is a measurement technique in which the effect of a pre- and post-selected system on a weakly interacting probe is magnified. In this thesis, I present the first experimental observation of WVA of a single photon. We observed that a signal photon - sent through a polarization interferometer and post-selected by photodetection in the almost-dark port - can act like eight photons. The effect of this single photon is measured as a nonlinear phase shift on a separate laser beam. The interaction between the two is mediated by a sample of laser- cooled 85Rb atoms. Electromagnetically induced transparency (EIT) is used to enhance the nonlinearity and overcome resonant absorption. I believe this work to be the first demonstration of WVA where a deterministic interaction is used to entangle two distinct optical systems. In WVA, the amplification is contingent on discarding a large portion of the original data set. While amplification increases measurement sensitivity, discarding data worsens it. Questioning whether these competing effects conspire to improve or diminish measurement accuracy has resulted recently in controversy. I address this question by calculating the maximum amount of information achievable with the WVA technique. By comparing this information to that achievable by the standard technique, where no post-selection is employed, I show that the WVA technique can be advantageous under a certain class of noise models. Finally, I propose a way to optimally apply the WVA technique.
Weak-value amplification (WVA) has emerged as an effective technique for detecting extremely small physical parameters by combining weak system–meter interactions with a carefully chosen post-selection strategy. In this paper, we explore how WVA performs when the meter is prepared in a Schrödinger cat-like state (SCS). Using the Fisher information (FI) as the primary figure of merit, we assess the attainable precision in estimating the interaction parameter. We compare the sensitivities of even coherent states (ECSs), odd coherent states (OCSs), and Yurke–Stoler states (YSSs) against coherent states (CS). We demonstrate that ECS and OCS as meters provide higher FI than the CS as a meter in some cases, depending on the measurement strategy. Also, ECS yields the largest conventional FI among the four meter states. Furthermore, we explore the impact of vacuum superposition with the meter on FI. We find that optimizing the vacuum coefficient enhances the FI in some conditions. This study shows that SCSs can be useful as meter states for improving precision in weak-measurement metrology.
The weak-value-amplification (WVA) technique has been extensively considered and debated in the field of quantum precision measurement, largely owing to the reduced Fisher information caused by the low probability of successful post-selection. %% In this work we show that, rather than the Gaussian meter state as typically considered, using the optical coherent state as a meter, the WVA measurement can definitely outperform the conventional measurement not involving the strategy of post-selection. %% We also show that the post-selection procedure involved in the WVA scheme can make a mixture of coherent states work better than a pure coherent state with identical average photon numbers. This is in sharp contrast to the claim proved in the absence of post-selection. The post-selection strategy can also result in the precision of Heisenberg (or even "super-Heisenberg") scaling with the photon numbers, but without using any expensive quantum resources. %% The present work may stimulate further investigations for the potential of the post-selection strategy in quantum precision measurements.
Amplification of the Schrödinger-cat state (even coherent-state superposition) can be accompanied by its non-exponential decoherence and strong squeezing effect in the degenerate optical parametric amplifier. In the classical pump approximation and small thermal noise limit, the Wigner function behaviour illustrates that this non-exponential effect is induced by the phase-selective character of amplification. The non-exponential decoherence is much slower, in contrast with phase-unselective amplification exhibiting faster exponential decay. Thus, if one is able to produce the Schrödinger-cat state with at least a small amplitude, then it can be partially amplified with only a weak decoherence effect.
The quantum Cheshire cat effect is an important phenomenon in quantum mechanics that reveals the separability of physical properties from their carriers. This effect transcends the classical framework whose attributes must be inherently attached to objects, providing new perspectives for quantum information and precision measurement. According to the quantum Cheshire cat effect, we prepare a pre-selected state of a spin-1/2 atomic system composed of two particles through a pre-selection process. We conduct quantum weak measurements on the spins and positions of these two atoms and extract weak values by using the method of imaginary time evolution (ITE). Subsequently, we perform post-selection on these two atoms and design two distinct post-selected states. Initially, we calculate analytical solutions when both atoms encounter these two different post-selected states separately. Then, during the stage of obtaining weak values via ITE, we first discuss the scenario with only one post-selected state. In this case, our experimental goal is to achieve spin exchange between the two atoms. We use ITE to obtain normalized coincidence rate for the system. By linearly fitting these normalized coincidence rate, we derive numerical solutions for the weak values of the system. The comparison between the analytical solutions and numerical results indicates that they are in close agreement, demonstrating that our method promotes spin exchange between the two atoms. Next, we examine scenarios involving both post-selected states in the post-selection process. After completing weak measurements on particles, delayed-choice allows them to evolve along different paths ultimately leading to distinct post-selected states. One particular post-selected state that results in final measurement outcomes indicates that the spin exchange occurs between both particles with amplification. Conversely, the other post-selected state ensures that even after undergoing weak measurement and delayed-choice, the states of the two particles remain consistent with their pre-measurement conditions. We also compare the analytical and numerical solutions of the experiment involving delayed choice and find that they are very consistent with each other. This consistency indicates that delayed-choice indeed has a significant influence on whether the final exchange occurs. Our research theoretically confirms the feasibility of fermionic systems within bipartite quantum Cheshire cat effects and illustrates how delayed-choice influences quantum Cheshire cat effects in spin-1/2 atomic systems.
Abstract Most studies for postselected weak measurement in optomechanical system focus on using a single photon as a measured system. However, we find that using weak coherent light instead of a single photon can also amplify the mirror’s position displacement of one photon. In the weak value amplification (WVA) regime, the weak value of one photon can lie outside the eigenvalue spectrum, proportional to the difference of the mirror’s position displacement between the successful and failed postselection and its successful postselection probability is dependent of the mean photon number of the coherent light and improved by adjusting it accordingly. Outside the WVA regime, the amplification limit can reach the level of the vacuum fluctuations, and when the mean photon number and the optomechanical coupling parameter are selected appropriately, its successful postselection probability becomes higher, which is beneficial to observe the maximum amplification value under the current experimental conditions. This result breaks the constraint that it is difficult to detect outside the WVA regime. This opens up a new regime for the study of a single photon nonlinearity in optomechanical system.