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arXiv:1311.6586 · Physical Review A

Quantum metrology via repeated quantum nondemolition measurements in a photon box

Yu-Ran Zhang, Jie-Dong Yue, Heng Fan

Published Feb 4, 2015• 2 citations
arXivHTMLPDF

Abstract

In quantum metrology schemes, one generally needs to prepare $m$ copies of $N$ entangled particles, such as entangled photon states, and then they are detected in a destructive process to estimate an unknown parameter. Here we present an experimental scheme for estimating this parameter by using repeated indirect quantum nondemolition measurements in the setup consisting of a photon in a superconducting cavity (called a photon box). This interaction-based scheme is able to achieve the phase sensitivity scaling as $1/N$ with a Fock state of $N$ photons. Moreover, we only need to prepare one initial $N$-photon state and it can be used repetitively for $m$ trials of measurements. This scheme is shown to sustain the quantum advantage for a much longer time than the damping time of Fock state and be more robust than the common strategy with exotic entangled states. To overcome the $2\ensuremath{\pi}/N$ periodic error in the estimation of the true parameter, we can employ a cascaded strategy by adding a real-time feedback interferometric layout.

DOI
10.1103/physreva.91.022104

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In quantum metrology schemes, one generally needs to prepare mmm copies of NNN entangled particles, such as entangled photon states, and then they are detected in a destructive process to estimate an unknown parameter. Here we present an experimental scheme for estimating this parameter by using repeated indirect quantum nondemolition measurements in the setup consisting of a photon in a superconducting cavity (called a photon box). This interaction-based scheme is able to achieve the phase sensitivity scaling as 1/N1/N1/N with a Fock state of NNN photons. Moreover, we only need to prepare one initial NNN-photon state and it can be used repetitively for mmm trials of measurements. This scheme is shown to sustain the quantum advantage for a much longer time than the damping time of Fock state and be more robust than the common strategy with exotic entangled states. To overcome the 2\ensuremathπ/N2\ensuremath{\pi}/N2\ensuremathπ/N periodic error in the estimation of the true parameter, we can employ a cascaded strategy by adding a real-time feedback interferometric layout.
The ubiquitous decoherence phenomenon is responsible for the lack of quantum superpositions at the macroscopic scale. It is increasingly difficult to isolate a quantum system from its environment when its size increases. Making use of the weird quantum properties of mesoscopic quantum states thus requires efficient means to combat decoherence. One option is real-time quantum feedback. It features the components of a conventional feedback: measurement of the system's state (sensor), analysis (controller), and feedback action (actuator) aiming to the target state. The random back-action of the measurements by the sensor makes quantum feedback much more difficult than its classical counterpart. Mesoscopic photon number (Fock) states feature a decoherence rate proportional to the photon number. They are thus a simple example of a fragile quantum resource. We demonstrated recently two quantum feedback schemes continuously stabilizing Fock state of a microwave field in a high-quality cavity. Sensitive atoms, crossing the field one at a time, are used as quantum nondemolition (QND) probes of its photon number. The feedback actuator is either a classical source [Sayrin et al., Nature (London) 477, 73 (2011)] or individual resonant atoms emitting or absorbing one photon each [Zhou et al., Phys. Rev. Lett. 108, 243602 (2012)]. Both schemes detect the quantum jumps of the photon number and efficiently correct their adverse effects, preparing and preserving a fragile quantum resource. We present an in-depth analysis of our methods, which sheds light onto the fundamental difficulties encountered in quantum feedback, in particular concerning the state estimation algorithm, and onto the ways to circumvent them. These results open the way to informationally optimal QND measurements or to the stabilization of mesoscopic field state superpositions. More generally, they can be cast in a variety of contexts to loosen the tight constraints set by decoherence in quantum metrology and quantum information processing.
Quantum metrology aims at achieving enhanced performance in measuring unknown parameters by utilizing quantum resources. Thus, quantum metrology is an important application of quantum technologies. Photonic systems can implement these metrological tasks with simpler experimental techniques. We present a scheme for improved parameter estimation by introducing entangled generalized coherent states (EGCS) for photonic quantum metrology. These states show enhanced sensitivity beyond the classical and Heisenberg limits and prove to be advantageous as compared to the entangled coherent and NOON states. Further, we also propose a scheme for experimentally generating certain entangled generalized coherent states with current technology.
We consider the estimation of a Hamiltonian parameter of a set of highly photosensitive samples, which are damaged after a few photons Nabs are absorbed, for a total time T . The samples are modelled as a two mode photonic system, where photons simultaneously acquire information on the unknown parameter and are absorbed at a fixed rate. We show that arbitrarily intense coherent states can obtain information at a rate that scales at most linearly with Nabs and T , whereas quantum states with finite intensity can overcome this bound. We characterise the quantum advantage as a function of Nabs and T , as well as its robustness to imperfections (non-ideal detectors, finite preparation and measurement rates for quantum photonic states). We discuss an implementation in cavity QED, where Fock states are both prepared and measured by coupling atomic ensembles to the cavities. We show that superradiance, arising due to a collective coupling between the cavities and the atoms, can be exploited for improving the speed and efficiency of the measurement.
Optical quantum metrology uses specially-prepared states of light to probe sensitive samples. Choosing a suitable probe state allows one to extract more information per probe photon about an unknown parameter than is possible using any classical technique. In effect, these techniques improve the sensitivity of the measurement whenever the number of probe photons is constrained in some way. This thesis presents experimental and theoretical results on the use of pairs of time-frequency entangled photons in precision measurements. It begins with an overview of necessary background knowledge about quantum optics and quantum information. This is followed by a theoretical discussion on the estimation of a single delay using two-photon interference. We show that constraints on the probe photon's bandwidth complicate the measurement problem, requiring suitable optimization of the two-photon quantum state to avoid losing precision. We then consider the use of two-photon interference for linear spectroscopic measurements. Linear spectroscopy relates the absorption and phase spectrum of a sample to unknown electronic parameters. We describe a proof-of-principle experiment demonstrating that two-photon interferometric spectroscopy can be used for simultaneously measurement of both absorption and phase. This is followed by an information-theoretic discussion of the precision of this technique. For low losses, we show that the method provides phase sensitivity similar to classical interferometry while approaching the optimal absorption precision of any possible measurement. If the absorption and phase values are both related to a single unknown parameter, then our technique provides improved sensitivity to this parameter compared to both classical measurements and other quantum techniques in the presence of realistic levels of loss. We conclude with a discussion of quantum-optical coherence tomography, which is a two-photon interferometric method for determining the material structure of a sample. We present an ongoing experiment which aims to apply the method to tissue-like samples, where the quantum measurement is limited by a poor signal-to-noise ratio. Preliminary results demonstrate that this noise can be largely reduced by suitable frequency-domain filtering. This allows us to precisely determine the position of a scattering center using a few hundred detected photon pairs despite the presence of large amounts of noise. We follow this with a theoretical discussion of signal artifacts which are known to complicate the measured interferogram. We show these artifacts are due to a distinct interferometric effect, which can be distinguished from the signal of interest using the relative time delay between detected photons. We conclude with a brief discussion on possible techniques for artifact removal.
Abstract Quantum metrology uses non-classical states, such as Fock states with a specific number of photons, to achieve an advantage over classical sensing methods. Typically, quantum metrological performance can be enhanced by increasing the involved excitation numbers, for example, by using large-photon-number Fock states. However, manipulating these states and demonstrating a quantum metrological advantage is experimentally challenging. Here we present an efficient method for generating large Fock states approaching 100 photons within a superconducting microwave cavity through the development of a programmable photon number filter. Using these states in displacement and phase measurements, we demonstrate quantum-enhanced metrology approaching the Heisenberg scaling for 40-photon Fock states and achieve a maximum metrological gain of up to 14.8 dB, highlighting the metrological advantages of large Fock states. Our study could be readily extended to mechanical and optical systems, promising potential applications in weak force detection and dark matter searches.
Leveraging quantum effects in metrology such as entanglement and coherence allows one to measure parameters with enhanced sensitivity. However, time-dependent noise can disrupt such Heisenberg-limited amplification. We propose a quantum-metrology method based on the quantum-signal-processing framework to overcome these realistic noise-induced limitations in practical quantum metrology. Our algorithm separates the gate parameter φφφ~(single-qubit Z phase) that is susceptible to time-dependent error from the target gate parameter θθθ~(swap-angle between |10> and |01> states) that is largely free of time-dependent error. Our method achieves an accuracy of 10−410^{-4}10−4 radians in standard deviation for learning θθθ in superconducting-qubit experiments, outperforming existing alternative schemes by two orders of magnitude. We also demonstrate the increased robustness in learning time-dependent gate parameters through fast Fourier transformation and sequential phase difference. We show both theoretically and numerically that there is an interesting transition of the optimal metrology variance scaling as a function of circuit depth ddd from the pre-asymptotic regime d≪1/θd \ll 1/θd≪1/θ to Heisenberg limit d→∞d \to \inftyd→∞. Remarkably, in the pre-asymptotic regime our method's estimation variance on time-sensitive parameter φφφ scales faster than the asymptotic Heisenberg limit as a function of depth, Var(φ^)≈1/d4\text{Var}(\hatφ)\approx 1/d^4Var(φ^​)≈1/d4. Our work is the first quantum-signal-processing algorithm that demonstrates practical application in laboratory quantum computers.