Quantum entanglement offers considerable advantages in how the sensitivity of interferometric precision scales with the resources available. However, when using entangled states it is important that a balance is found between the phase sensitivity of the state and its robustness to particle loss. Recent work (Dorner et al 2009 Phys. Rev. Lett. 102 040403) has optimized this balance and found the ideal initial state for any given loss rate in a two-path interferometer. Here we describe a route towards achieving precisions close to that of the theoretical optimum by using beam splitters with variable reflectivity. We also discuss how adopting a multipath approach may prove to be important in future metrology schemes that aim to surpass the standard quantum limit.
Quantum entanglement offers considerable advantages in how the sensitivity of interferometric precision scales with the resources available. However, when using entangled states it is important that a balance is found between the phase sensitivity of the state and its robustness to particle loss. Recent work (Dorner et al 2009 Phys. Rev. Lett. 102 040403) has optimized this balance and found the ideal initial state for any given loss rate in a two-path interferometer. Here we describe a route towards achieving precisions close to that of the theoretical optimum by using beam splitters with variable reflectivity. We also discuss how adopting a multipath approach may prove to be important in future metrology schemes that aim to surpass the standard quantum limit.
This paper explores the sensitivity gains afforded by spin-squeezed states in atom interferometry, in particular using Bragg diffraction. We introduce a generalised input-output formalism that accurately describes realistic, non-unitary interferometers, including losses due to velocity selectivity and scattering into undesired momentum states. This formalism is applied to evaluate the performance of one-axis twisted spin-squeezed states in improving phase sensitivity. Our results show that by carefully optimising the parameters of the Bragg beam splitters and controlling the degree of squeezing, it is possible to improve the sensitivity of the interferometer by several dB with respect to the standard quantum limit despite realistic levels of losses in light pulse operations. However, the analysis also highlights the challenges associated with achieving these improvements in practice, most notably the impact of finite temperature on the benefits of entanglement. The results suggest ways of optimising interferometric setups to exploit quantum entanglement under realistic conditions, thereby contributing to advances in precision metrology with atom interferometers.
The ability to make ultra-precise measurements is fundamentally important to science as it allows theories to be tested and refined. Interferometers offer unrivalled measurement precision and therefore form the basis of many metrology schemes. Research has shown that by using quantum states as inputs to interferometers, precisions better than anything possible classically can be achieved. Nevertheless, these states are difficult to produce and fragile to particle losses. Consequently, classical inputs, which are extremely robust, are used in experiments. Here, however, we propose experimentally accessible schemes to make quantum-limited measurements, in particular rotation measurements using Bose-Einstein condensates, that are robust to losses. We begin by describing how, by loading a Bose-Einstein condensate into an optical ring lattice, multiport beam splitters are created through a simple raising and lowering of potential barriers between sites. We then use these ‘splitters’ to create an atomic gyroscope. We demonstrate how to create several quantum states in the gyroscope, all capable of making rotation measurements. Whilst NOON states afford best precision in idealised set-ups, we find they are outperformed by ‘bat’ states for modest loss rates. However, bat states are not ideal as they are outperformed by classical states for large losses. A second gyroscope scheme is therefore developed. Using multiple momentum modes, rather than just two, we show quantum-limited precisions can be reached using states that have similar robustness to classical states. The final section focuses on the precision of linear interferometers. Recent work[1, 2] has calculated the theoretical optimum initial states for two-mode lossy interferometers. Here we present an experimental way to produce initial states that afford similar precisions to this optimum. We also consider lossy multimode interferometry and demonstrate a potential advantage over two-mode systems. It is thought with further investigation other advantages will be found.
We optimize two-mode entangled number states of light in the presence of loss in order to maximize the extraction of the available phase information in an interferometer. Our approach optimizes over the entire available input Hilbert space with no constraints, other than fixed total initial photon number. We optimize to maximize the Fisher information, which is equivalent to minimizing the phase uncertainty. We find that in the limit of zero loss, the optimal state is the maximally path-entangled (so-called N00N) state, for small loss, the optimal state gradually deviates from the N00N state, and in the limit of large loss, the optimal state converges to a generalized two-mode coherent state, with a finite total number of photons. The results provide a general protocol for optimizing the performance of a quantum optical interferometer in the presence of photon loss, with applications to quantum imaging, metrology, sensing, and information processing.
The hybrid interferometer, integrating an optical parametric amplifier and a beam splitter, exhibits the potential to outperform the SU(1,1) interferometer. However, photon loss remains a key constraint for practical implementation. To address this challenge, we propose a quantum metrology scheme that utilizes multi-photon subtraction at the output and replaces the standard 50:50 beam splitter with a variable beam splitter—thereby enhancing robustness to photon loss. We adopt a coherent state (injected into mode a or b ) and a vacuum state as inputs to the interferometer, while performing homodyne detection. Our results demonstrate that the selection of input modes exerts a significant influence on phase estimation, and the optimization of the beam splitter’s transmittance is essential to maximize phase sensitivity under lossy conditions. Furthermore, photon subtraction notably enhances phase sensitivity, quantum Fisher information, and noise robustness. Notably, our scheme attains sensitivities exceeding the Heisenberg limit even in the presence of 20% photon loss.
Entanglement is an important quantum resource to achieve high-sensitivity quantum metrology. However, the rapid decoherence of quantum entangled states, due to the unavoidable environmental noise, results in practically the unwanted sharp drop of the measurement sensitivity. To overcome such a difficulty, here we propose a spin-oscillator hybrid quantum interferometer to achieve the desirable precise estimation of the parameter encoded in the vibrations of the oscillator. Differing from the conventional two-mode quantum interferometers input by the two-mode NOON state or entangled coherent states, whose achievable sensitivities are strongly limited by the decoherence of the entangled vibrational states, we demonstrate that the present interferometer, input by a spin-dependent two-mode entangled state, possesses a manifest advantage; i.e., the measurement sensitivity of the estimated parameter is not influenced by the decoherence from the spin-oscillator entanglement. This is because, by applying a spin-oscillator disentangled operation, the information of the estimated parameter encoded originally in the vibrational degrees can be effectively transferred into the spin degree and then can be sensitively estimated by the precise spin-state population measurements. As consequence, the proposed hybrid quantum interferometer possesses manifest robustness against the particle losses of the vibrational modes. Interestingly, the achieved phase measurement sensitivity can still surpass the standard quantum limit obviously, even if a relatively large number of particle loss occurs in one of the two modes. The potential application of the proposed spin-oscillator hybrid quantum interferometer is also discussed.
Abstract We propose a quantum-enhanced metrological scheme utilizing unbalanced entangled coherent states (ECSs) generated by passing a coherent state and a coherent state superposition through an unbalanced beam splitter (BS). We identify the optimal phase sensitivity of this scheme by maximizing the quantum Fisher information (QFI) with respect to the BS transmission ratio. Our scheme outperforms the conventional scheme with a balanced BS, particularly in the presence of single-mode photon loss. Notably, our scheme retains quantum advantage in phase sensitivity in the limit of high photon intensity, where the balanced scheme offers no advantage over the classical strategy.