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Register a new userEntangled Fock states for Robust Quantum Optical Metrology, Imaging, and Sensing
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We propose a class of path-entangled photon Fock states for robust quantum optical metrology, imaging, and sensing in the presence of loss. We model propagation loss with beam-splitters and derive a reduced density matrix formalism from which we examine how photon loss affects coherence. It is shown that particular entangled number states, which contain a special superposition of photons in both arms of a Mach-Zehnder interferometer, are resilient to environmental decoherence. We demonstrate an order of magnitude greater visibility with loss, than possible with N00N states. We also show that the effectiveness of a detection scheme is related to super-resolution visibility.
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Over the past 20 years, bright sources of entangled photons have led to a renaissance in quantum optical interferometry. Optical interferometry has been used to test the foundations of quantum mechanics and implement some of the novel ideas associated with quantum entanglement such as quantum teleportation, quantum cryptography, quantum lithography, quantum computing logic gates, and quantum metrology. In this paper, we focus on the new ways that have been developed to exploit quantum optical entanglement in quantum metrology to beat the shot-noise limit, which can be used, e.g., in fiber optical gyroscopes and in sensors for biological or chemical targets. We also discuss how this entanglement can be used to beat the Rayleigh diffraction limit in imaging systems such as in LIDAR and optical lithography.
To acquire the best path-entangled photon Fock states for robust quantum optical metrology with parity detection, we calculate phase information from a lossy interferometer by using twin entangled Fock states. We show that (a) when loss is less than 50% twin entangled Fock states with large photon number difference give higher visibility while when loss is higher than 50% the ones with less photon number difference give higher visibility; (b) twin entangled Fock states with large photon number difference give sub-shot-noise limit sensitivity for phase detection in a lossy environment. This result provides a reference on what particular path-entangled Fock states are useful for real world metrology applications.
We study how useful random states are for quantum metrology, i.e., surpass the classical limits imposed on precision in the canonical phase estimation scenario. First, we prove that random pure states drawn from the Hilbert space of distinguishable particles typically do not lead to super-classical scaling of precision even when allowing for local unitary optimization. Conversely, we show that random states from the symmetric subspace typically achieve the optimal Heisenberg scaling without the need for local unitary optimization. Surprisingly, the Heisenberg scaling is observed for states of arbitrarily low purity and preserved under finite particle losses. Moreover, we prove that for such states a standard photon-counting interferometric measurement suffices to typically achieve the Heisenberg scaling of precision for all possible values of the phase at the same time. Finally, we demonstrate that metrologically useful states can be prepared with short random optical circuits generated from three types of beam-splitters and a non-linear (Kerr-like) transformation.
It has been proposed and demonstrated that path-entangled Fock states (PEFSs) are robust against photon loss over NOON states [S. D. Huver emph{et al.}, Phys. Rev. A textbf{78}, 063828 (2008)]. However, the demonstration was based on a measurement scheme which was yet to be implemented in experiments. In this work, we quantitatively illustrate the advantage of PEFSs over NOON states in the presence of photon losses by analytically calculating the quantum Fisher information. To realize such an advantage in practice, we then investigate the achievable sensitivities by employing three types of feasible measurements: parity, photon-number-resolving, and homodyne measurements. We here apply a double-port measurement strategy where the photons at each output port of the interferometer are simultaneously detected with the aforementioned types of measurements.
We develop general tools to characterise and efficiently compute relevant observables of multimode $N$-photon states generated in non-linear decays in one-dimensional waveguides. We then consider optical interferometry in a Mach-Zender interferometer where a $d$-mode photonic state enters in each arm of the interferometer. We derive a simple expression for the Quantum Fisher Information in terms of the average photon number in each mode, and show that it can be saturated by number-resolved photon measurements that do not distinguish between the different $d$ modes.
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