n n n The precision of physical parameters is fundamentally limited by irreducible levelsof noise set by quantum mechanics. Quantum metrology is the study of reaching theselimits of noise by employing optimal schemes for parameter estimation. Techniquesin quantum metrology can assist in developing devices to measure the fundamentalinterplay between quantum mechanics and general relativity at state-of-the-artprecision. An example of this is the recent detection of gravitational waves bythe LIGO interferometer. In this thesis, we focus on using quantum metrologyfor estimating space-time parameters. We show the optimal quantum resourcesthat are needed for estimating the gravitational redshift of light propagating in theSchwarzschild space-time of Earth including the inevitable losses due to atmosphericdistortion. We also propose a quantum interferometer using higher order Kerrnon-linearities to improve the sensitivity of estimating gravitational time dilation.In principle, we would be able to downsize interferometers and probe gravity over asmall scale potentially making it practical for measuring gravitational gradients. Wethen study the interesting features of the metric around a rotating massive bodyknown as the Kerr metric and propose implementing a stationary interferometer tomeasure the effect of frame dragging. Finally, we consider loss in the visibility ofquantum interference of single photons in rotating reference frames, and analogouslyin the Kerr metric. In essence, the quantum interference of photons will be affectedby the relativistic effect of rotation. We find experimentally feasible parametersrequiring long optical fibre for long coherence lengths of photons. Our results willhopefully contribute to the efforts of building future quantum technologies that willenter a new regime where general relativistic effects can be measured.
n n n The precision of physical parameters is fundamentally limited by irreducible levelsof noise set by quantum mechanics. Quantum metrology is the study of reaching theselimits of noise by employing optimal schemes for parameter estimation. Techniquesin quantum metrology can assist in developing devices to measure the fundamentalinterplay between quantum mechanics and general relativity at state-of-the-artprecision. An example of this is the recent detection of gravitational waves bythe LIGO interferometer. In this thesis, we focus on using quantum metrologyfor estimating space-time parameters. We show the optimal quantum resourcesthat are needed for estimating the gravitational redshift of light propagating in theSchwarzschild space-time of Earth including the inevitable losses due to atmosphericdistortion. We also propose a quantum interferometer using higher order Kerrnon-linearities to improve the sensitivity of estimating gravitational time dilation.In principle, we would be able to downsize interferometers and probe gravity over asmall scale potentially making it practical for measuring gravitational gradients. Wethen study the interesting features of the metric around a rotating massive bodyknown as the Kerr metric and propose implementing a stationary interferometer tomeasure the effect of frame dragging. Finally, we consider loss in the visibility ofquantum interference of single photons in rotating reference frames, and analogouslyin the Kerr metric. In essence, the quantum interference of photons will be affectedby the relativistic effect of rotation. We find experimentally feasible parametersrequiring long optical fibre for long coherence lengths of photons. Our results willhopefully contribute to the efforts of building future quantum technologies that willenter a new regime where general relativistic effects can be measured.
Searches for fundamental physics such as gravitational waves, dark matter, and quantum gravity are now reaching the quantum limit around a century since the invention of quantum mechanics. To push past the fundamental quantum noise and accelerate the discovery of new physics, we need to understand and exploit the interplay of quantum information and quantum metrology. In this thesis, we advocate for a new perspective on the design of gravitational-wave interferometers and other precision waveform sensors, one centred on optimising the sensitivity through studying and manipulating the relevant quantum information-theoretic quantities with practical considerations for loss and classical noise. We demonstrate this approach with a series of papers proposing various measurement schemes, initial quantum states, and quantum control sequences to achieve the fundamental quantum limits of different waveform estimation problems. We suggest that the ultimate potential sensitivity of present experimental designs remains untapped: present in the capability of the device but not yet accessed. In particular, we show that a quantum advantage exists in sensing non-stationary or stochastic waveform signals or those with a wide range of possible frequencies. We discuss the implications of these results and how to realise them for future searches for fundamental physics.
In this thesis we study relativistic effects on quantum systems. Quantum physics in curved spacetime is reviewed in a first place, with a focus on continuous variables formalism, quantum metrology techniques, and the relativistic treatment of polarised photons. Then, three topics of interest are studied. The first one is the phononic gravitational wave detector, where resonant mode-mixing and particle creation are triggered in a Bose-Einstein condensate by the passing of a gravitational wave, which can then be measured thanks to quantum metrology techniques. The theory for the phonons’ transformation is developed in details in different resonance scenarios and some sources of noise are considered, like shaking of the cavity where the condensate is trapped and thermal noise. The second topic adressed is quantum communication and metrology in space. In this part, we describe quantum experiments involving communications between Earth and satellites using frequency modes of photons. The propagated and measured photons encode parameters of the spacetime background that can be measured using quantum metrology. Several satellite schemes are discussed, such as satellite to satellite radial communications in Kerr spacetime or Earth to satellite communications in Schwarzschild spacetime. The last topic of this thesis is the evolution of helicity states of photons in a relativistic picture. Two experiments are considered: one where the photons propagate between Earth and satellites through the curved spacetime background surrounding the Earth. The other experiment looks at quantum states of polarised photons as seen by centrifuged observers. For each of these parts, we provide the theory for novel experimental proposals, within the frameworks of either (or both) quantum communications and quantum metrology, that, we believe, would lead to a better understanding in the overlap of quantum mechanics and the relativity theories.
We consider quantum communication schemes where quantum optical signals are exchanged between a source on Earth and a satellite. The background curved spacetime affects the quantum state of the propagating photons. We employ quantum-metrology techniques to obtain optimal bounds for the precision of quantum measurements of relevant physical parameters encoded in the final state. We focus on satellites in low Earth orbits and we find that our scheme improves the precision of the measurement of the Schwarzschild radius obtained within previous studies. Therefore, our techniques can provide the theoretical tools for novel developments that can potentially outperform the state-of-the-art obtained through classical means. We also review the impact of the relativistic effects on a simple quantum key distribution protocol within satellite schemes and find that such effects can be greatly damaging if they are not properly accounted for.
The creation of delocalized coherent superpositions of quantum systems experiencing di erent relativistic e ects is an important milestone in future research at the interface of gravity and quantum mechanics. This could be achieved by generating a superposition of quantum clocks that follow paths with di erent gravitational time dilation and investigating the consequences on the interference signal when they are eventually recombined. Light-pulse atom interferometry with elements employed in optical atomic clocks is a promising candidate for that purpose, but su ers from major challenges including its insensitivity to the gravitational redshift in a uniform eld. All these di- culties can be overcome with a novel scheme presented here which is based on initializing the clock when the spatially separate superposition has already been generated and performing a doubly differential measurement where the di erential phase shift between the two internal states is compared for di erent initialization times. This can be exploited to test the universality of the gravitational redshift (UGR) with delocalized coherent superpositions of quantum clocks and it is argued that its experimental implementation should be feasible with a new generation of 10-meter atomic fountains that will soon become available. Interestingly, the approach also o ers signi cant advantages for more compact set-ups based on guided interferometry or hybrid con gurations. Furthermore, in order to provide a solid foundation for the analysis of the various interferometry schemes and the e ects that can be measured with them, a general formalism for a relativistic description of atom interferometry in curved spacetime is developed. It can deal with freely falling atoms, but also include the e ects of external forces and guiding potentials, and can be applied to a very wide range of situations. As an important ingredient for quantum-clock interferometry, suitable difraction mechanisms for atoms in internal-state superpositions are investigated too. Finally, the relation of the proposed doubly-di erential measurement scheme to other experimental approaches and to tests of the universality of free fall (UFF) is discussed in detail.
Precision interferometry with quantum states has emerged as an essential tool for experimentally answering fundamental questions in physics. Optical quantum interferometers are of particular interest because of mature methods for generating and manipulating quantum states of light. Their increased sensitivity promises to enable tests of quantum phenomena, such as entanglement, in regimes where tiny gravitational effects come into play. However, this requires long and decoherence-free processing of quantum entanglement, which, for large interferometric areas, remains unexplored territory. Here, we present a table-top experiment using maximally path-entangled quantum states of light in a large-scale interferometer sensitive enough to measure the rotation rate of Earth. The achieved sensitivity of 5 μrad s −1 constitutes the highest rotation resolution ever reached with optical quantum interferometers. Further improvements to our methodology will enable measurements of general-relativistic effects on entangled photons, allowing the exploration of the interplay between quantum mechanics and general relativity, along with tests for fundamental physics.
Precise measurement of physical quantities plays a crucial role in the development of science and technology.The main purpose of the dissertation is two-fold: to investigate the ultimate precision for estimation of physical quantities using Gaussian states and to propose an efficient method for certification of Bayesian error region in general quantum parameter estimation.In the first part, we begin with analyzing sensitivity for estimating a phase difference in an optical interferometer.Optical interferometry is widely used in science and industry for measuring small displacements.Recently, a large-scale optical interferometer socalled the Laser interferometer Gravitational-Wave Observatory (LIGO) has succeeded in detecting a gravitational wave, the signal of which is extremely small.On the other hand, it has been shown that a non-classical feature of quantum states can improve the sensitivity of estimation, such as in optical interferometer, including the LIGO.From a practical point of view, we inspect the practically achievable precision using non-classical Gaussian states in Mach-Zehnder interferometer with feasible measurements and realistic photon loss.We then investigate the precision of single-mode phase estimation using Gaussian measurement, which can be realized by using homodyne detection, and i show that non-Gaussian measurement is necessary to utilize the power of Gaussian input probes optimally.Finally, we find the optimal measurement for general Gaussian quantum metrology and identify three distinct optimal measurements corresponding to different circumstances.In the second part, we study the Bayesian error region, which is a crucial concept for a general estimation process.When estimating a physical quantity, one has to supply the error interval (single-parameter) or error region (multi-parameter) as well as the estimate.However, it has been shown that as the dimension of quantum systems of interest grows, it becomes intractable to calculate the size and credibility of Bayesian error regions.As an alternative, we derive an analytical expression for the properties, the size and credibility, of Bayesian error regions, in an asymptotic regime.We then propose an efficient numerical method to calculate them for high-dimensional quantum systems even in a non-asymptotic regime.