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arXiv:1910.02595 · Laser Physics Letters

The influence of the Earth’s curved spacetime on Gaussian quantum coherence

Tonghua Liu, Shuo Cao, Shumin Wu, Haosheng Zeng

Published Jul 23, 2019• 13 citations
arXivHTMLPDF

Abstract

Abstract Light wave-packets propagating from the Earth to satellites will be deformed by the curved background spacetime of the Earth, thus influencing the quantum state of light. We show that Gaussian coherence of photon pairs, which are initially prepared in a two-mode squeezed state, is affected by the curved spacetime background of the Earth. We demonstrate that quantum coherence of the state increases for a specific range of height h and then gradually approaches a finite value with further increasing height of the satellite’s orbit in Kerr spacetime, because special relativistic effects are involved. Meanwhile, we find that Gaussian coherence increases with the increase of Gaussian bandwidth parameter, but the Gaussian coherence decreases with the growth of the peak frequency. In addition, we also find that total gravitational frequency shift causes changes of Gaussian coherence less than and different initial peak frequencies also can effect the rate of change with the satellite height in geostationary Earth orbits.

DOI
10.1088/1612-202x/ab2be4

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Abstract Light wave-packets propagating from the Earth to satellites will be deformed by the curved background spacetime of the Earth, thus influencing the quantum state of light. We show that Gaussian coherence of photon pairs, which are initially prepared in a two-mode squeezed state, is affected by the curved spacetime background of the Earth. We demonstrate that quantum coherence of the state increases for a specific range of height h and then gradually approaches a finite value with further increasing height of the satellite’s orbit in Kerr spacetime, because special relativistic effects are involved. Meanwhile, we find that Gaussian coherence increases with the increase of Gaussian bandwidth parameter, but the Gaussian coherence decreases with the growth of the peak frequency. In addition, we also find that total gravitational frequency shift causes changes of Gaussian coherence less than and different initial peak frequencies also can effect the rate of change with the satellite height in geostationary Earth orbits.
Abstract Spacetime curvature of the Earth deforms wave packets of photons sent from the Earth to satellites, thus influencing the quantum state of light. We show that Gaussian steering of photon pairs, which are initially prepared in a two‐mode squeezed state, is affected by the curved spacetime background of the Earth. We demonstrate that quantum steerability of the state increases for a specific range of height h and then gradually approaches a finite value with further increasing height of the satellite's orbit. Comparing with the peak frequency parameter, the Gaussian steering changes more for different squeezing parameters, while the gravitational frequency effect leads to quantum steering asymmetry between the photon pairs. In addition, we find that the influence of spacetime curvature on the steering in the Kerr spacetime is very different from the non‐rotating case because special relativistic effects are involved.
The preparation of quantum systems and the execution of quantum information tasks between distant users are always affected by gravitational and relativistic effects. In this work, we quantitatively analyze how the curved space-time background of the Earth affects the classical and quantum correlations between photon pairs that are initially prepared in a two-mode squeezed state. More specifically, considering the rotation of the Earth, the space-time around the Earth is described by the Kerr metric. Our results show that these state correlations, which initially increase for a specific range of satellite's orbital altitude, will gradually approach a finite value with increasing height of satellite's orbit (when the special relativistic effects become relevant). More importantly, our analysis demonstrates that the changes of correlations generated by the total gravitational frequency shift could reach the level of [Formula: see text] within the satellite's height at geostationary Earth orbits.
We investigate the interplay between gravity and the quantum coherence present in the state of a pulse of light propagating in curved spacetime. We first introduce an operational way to distinguish between the overall shift in the pulse wave packet and its genuine deformation after propagation. We then apply our technique to quantum states of photons that are coherent in the frequency degree of freedom, as well as to states of completely incoherent light. We focus on Gaussian profiles and frequency combs and find that the quantum coherence initially present can enhance the deformation induced by propagation in a curved background. These results further support the claim that genuine quantum features, such as quantum coherence, can be used to probe the gravitational properties of physical systems. We specialize our techniques to Earth-to-satellite communication setups, where the effects of gravity are weak but can be tested with current satellite technologies.
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 study how quantum systems that propagate in the spacetime of a rotating planet are affected by the curved background. Spacetime curvature affects wavepackets of photons propagating from Earth to a satellite, and the changes in the wavepacket encode the parameters of the spacetime. This allows us to evaluate quantitatively how quantum communications are affected by the curved spacetime background of the Earth and to achieve precise measurements of Earth's Schwarzschild radius and equatorial angular velocity. We then provide a comparison with the state of the art in parameter estimation obtained through classical means. Satellite to satellite communications and future directions are also discussed.
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.