By creating superpositions in a Hilbert space consisting of many modes, rather than just two, phase shifts can be measured with Heisenberg limited precision and have similar robustness to particle loss as unentangled states. Previous proposals for measuring phase shifts with Heisenberg limited precision require a two-mode highly entangled state, for example a NOON state. Unfortunately these states rapidly lose their precision when decoherence effects such as particle loss are accounted for. Here we propose a way to use a multimode superposition state to measure rates of rotation in the presence of loss with unprecedented precision using an ultra-cold atomic gas.
By creating superpositions in a Hilbert space consisting of many modes, rather than just two, phase shifts can be measured with Heisenberg limited precision and have similar robustness to particle loss as unentangled states. Previous proposals for measuring phase shifts with Heisenberg limited precision require a two-mode highly entangled state, for example a NOON state. Unfortunately these states rapidly lose their precision when decoherence effects such as particle loss are accounted for. Here we propose a way to use a multimode superposition state to measure rates of rotation in the presence of loss with unprecedented precision using an ultra-cold atomic gas.
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.
By exploiting the correlation properties of ultracold atoms in a multimode interferometer, we show how quantum enhanced measurement precision can be achieved with strong robustness to particle loss. While the potential for enhanced measurement precision is limited for even moderate loss in two-mode schemes, multimode schemes can be more robust. A ring interferometer for sensing rotational motion with noninteracting fermionic atoms can realize an uncertainty scaling of 1/(N√η) for N particles with a fraction η remaining after loss, which undercuts the shot-noise limit of two-mode interferometers. A second scheme with strongly interacting bosons achieves a comparable measurement precision and improved readout.
In optical interferometry path-entangled states such as NOON states have shown to give quantum-enhanced precision measurements, but these states are notoriously fragile to particle losses, which typically collapse the quantum state and destroy the phase information. A class of inherently robust states that show the potential for great improvements over the alternatives are the entangled coherent states (ECSs). We show that these states allow substantial improvements over unentangled `classical' states and highly-entangled NOON states for a wide range of loss values. We then describe a measurement scheme that can be used to measure these states with a precision close to the theoretical bound given by the quantum Fisher information. \nWe then look at the quantum mechanisms that lead to precise measurements. In optical interferometry multi-mode entanglement is often assumed to be the driving force behind quantum enhanced measurements. Recent work has shown this assumption to be false, and here we show that when photon losses occur multi-mode entanglement is actually detrimental to obtaining quantum enhanced measurements. We specifically apply this idea to a superposition of coherent states, demonstrating that these states show a robustness to loss that allows them to significantly outperform their competitors in realistic systems. A practically viable measurement scheme is then presented that allows measurements close to the theoretical bound, even with loss. \nIn this thesis we also consider superpositions of spin coherent states and their application to quantum metrology. Compared to optical states, spin systems have a distinctly different process of decoherence known as non-Markovian dephasing, which has shown to give greatly improved robustness to loss. We see that spin cat states give an enhanced scaling over the shot noise limit, even with dephasing, whilst being realisable with current technology.
Quantum entanglement offers the possibility of making measurements beyond the classical limit, however some issues still need to be overcome before it can be applied in realistic lossy systems. Recent work has used the quantum Fisher information (QFI) to show that entangled coherent states (ECSs) may be useful for this purpose as they combine sub-classical phase precision capabilities with robustness (Joo et al., 2011). However, to date no effective scheme for measuring a phase in lossy systems using an ECS has been devised. Here we present a scheme that does just this. We show how one could measure a phase to a precision significantly better than that attainable by both unentangled "classical" states and highly-entangled NOON states over a wide range of different losses. This brings quantum metrology closer to being a realistic and practical technology.
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 Two-mode interferometers lay the foundations for quantum metrology. Instead of exploring quantum entanglement in the two-mode interferometers, a single bosonic mode also promises a measurement precision beyond the shot-noise limit (SNL) by taking advantage of the infinite-dimensional Hilbert space of Fock states. Here, we demonstrate a single-mode phase estimation that approaches the Heisenberg limit (HL) unconditionally. Due to the strong dispersive nonlinearity and long coherence time of a microwave cavity, quantum states of the form (∣0⟩+∣N⟩)/2 0 + N ∕ 2 can be generated, manipulated and detected with high fidelities, leading to an experimental phase estimation precision scaling as ∼ N −0.94 . A 9.1 dB enhancement of the precision over the SNL at N = 12 is achieved, which is only 1.7 dB away from the HL. Our experimental architecture is hardware efficient and can be combined with quantum error correction techniques to fight against decoherence, and thus promises quantum-enhanced sensing in practical applications.