Abstract
This chapter describes two proposals for practical realisation of the thought experiment form the previous Chapter, with interfering “clocks” subject to time dilation.
This chapter is based on and contains material from: Quantum interferometric visibility as a witness of general relativistic proper time, M. Zych, F. Costa, I Pikovski, and Č. Brukner, Nature Commun. 2:505 doi:10.1038/ncomms1498 (2011); and General relativistic effects in quantum interference of photons, M. Zych, F. Costa, I. Pikovski, T. C. Ralph, and Č. Brukner, Class. Quant. Grav. 29, 224010 (2012).
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Notes
- 1.
In a typical interferometric scenario, e.g. in atomic fountains, this assumption is satisfied [1].
- 2.
Time evolution of any observable in quantum theory is given by the commutator of the observable with the Hamiltonian. Thus, rate of evolution of any internal observable will be modified by the same factor by which the rest frame Hamiltonian is rescaled.
- 3.
For a bipartite pure quantum state the purity of the reduced density matrix is a measure of entanglement and \(\mathcal V\) also quantifies the purity of the reduced state, see also Eq. (4.15).
- 4.
By a faraway observer is here considered an observer at a large enough radial distance from the mass, such that locally measured times and distances are arbitrary close to the coordinate time and distance—for the Schwarzschild space-time considered in this work \(|g_{\mu \nu }|\rightarrow 1\) for \(r\rightarrow \infty \).
- 5.
Proposal to probe gravitationally induced phase shift of classical light in a laboratory experiment was first formulated in Ref. [28], but has not yet been realised.
- 6.
Defining two wave packets to be distinguishable when the absolute value of the amplitude between them is 1 / n yields \(\mathcal V_n = n^{-(\Delta \tau /t_{n\perp })^2}\) where \(t_{n\perp } = 2 \log (n) \sqrt{\sigma }\) is the corresponding clock’s precision.
- 7.
Note, that classical models of light have already been extensively disproved experimentally, but only in regimes where no effect of GR is present.
- 8.
Note that the Pound-Rebka experiment [39] probed the same aspect of GR: the redshift can be explained as each photon having a gravitational potential energy of \(g h E /c^2\), with \(E=\hbar \nu \). The redshift is then a consequence of the (semi-classical) mass-energy equivalence and energy conservation. However, the quantum nature of the photons was not probed directly in the Pound-Rebka experiment, which is thus still consistent with a classical description of light (more precisely, the experiment is consistent with classical waves on a curved background or with classical particles in a Newtonian potential, see Fig. 5.5 and Chap. 1). Measuring the gravitational phase shift in single photon interference would allow probing this aspect of GR in a quantum regime. In simple terms, it would provide a quantum extension of the Pound-Rebka experiment in the same way as the COW experiment [6] was a quantum extension of Galilei’s free fall experiments.
References
A. Peters, K.Y. Chung, S. Chu, High-precision gravity measurements using atom interferometry. Metrologia 38, 25 (2001)
N. Margolus, L.B. Levitin, The maximum speed of dynamical evolution. Phys. D: Nonlinear Phenom. 120, 188–195 (1998). Proceedings of the Fourth Workshop on Physics and Consumption
P. Kosiński, M. Zych, Elementary proof of the bound on the speed of quantum evolution. Phys. Rev. A 73, 024303 (2006)
B. Zieliński, M. Zych, Generalization of the Margolus-Levitin bound. Phys. Rev. A 74, 034301 (2006)
S. Wajima, M. Kasai, T. Futamase, Post-Newtonian effects of gravity on quantum interferometry. Phys. Rev. D 55, 1964 (1997)
R. Colella, A. Overhauser, S. Werner, Observation of gravitationally induced quantum interference. Phys. Rev. Lett. 34, 1472–1474 (1975)
Y. Aharonov, D. Bohm, Significance of electromagnetic potentials in the quantum theory. Phys. Rev. 115, 485–491 (1959)
V.B. Ho, M.J. Morgan, An experiment to test the gravitational Aharonov-Bohm effect. Aust. J. Phys. 47, 245–252
C.M. Will, Theory and Experiment in Gravitational Physics (Cambridge University Press, 1993)
M. Zawisky, M. Baron, R. Loidl, H. Rauch, Testing the world’s largest monolithic perfect crystal neutron interferometer. Nucl. Instrum. Meth. Phys. Res., Sect. A 481, 406–413 (2002)
A. Peters, K.Y. Chung, S. Chu, Measurement of gravitational acceleration by dropping atoms. Nature 400, 849–852 (1999)
H. Müller, S.-W. Chiow, S. Herrmann, S. Chu, Atom interferometers with scalable enclosed area. Phys. Rev. Lett. 102, 240403 (2009)
I. Neder, M. Heiblum, D. Mahalu, V. Umansky, Entanglement, dephasing, and phase recovery via cross-correlation measurements of electrons. Phys. Rev. Lett. 98, 036803 (2007)
Y. Ji, Y. Chung, D. Sprinzak, M. Heiblum, D. Mahalu, H. Shtrikman, An electronic Mach-Zehnder interferometer. Nature 422, 415–418 (2003)
M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. Van der Zouw, A. Zeilinger, Wave-particle duality of C60 molecules. Nature 401, 680–682 (1999)
S. Gerlich, S. Eibenberger, M. Tomandl, S. Nimmrichter, K. Hornberger, P.J. Fagan, J. Tüxen, M. Mayor, M. Arndt, Quantum interference of large organic molecules. Nat. Commun. 2, 263 (2011)
J.R. Miller, The NHMFL 45-T hybrid magnet system: past, present, and future. IEEE Trans. Appl. Supercond. 13, 1385–1390 (2003)
T. Kovachy, P. Asenbaum, C. Overstreet, C. Donnelly, S. Dickerson, A. Sugarbaker, J. Hogan, M. Kasevich, Quantum superposition at the half-metre scale. Nature 528, 530–533 (2015)
H. Müller, A. Peters, S. Chu, A precision measurement of the gravitational redshift by the interference of matter waves. Nature 463, 926–929 (2010)
S. Dimopoulos, P.W. Graham, J.M. Hogan, M.A. Kasevich, General relativistic effects in atom interferometry. Phys. Rev. D 78, 042003 (2008)
S. Fray, C.A. Diez, T.W. Hänsch, M. Weitz, Atomic interferometer with amplitude gratings of light and its applications to atom based tests of the equivalence principle. Phys. Rev. Lett. 93, 240404 (2004)
H. Müller, S.-W. Chiow, S. Herrmann, S. Chu, K.-Y. Chung, Atom-interferometry tests of the isotropy of post-Newtonian gravity. Phys. Rev. Lett. 100, 031101 (2008)
D.M. Greenberger, Theory of particles with variable mass. I. Formalism. J. Math. Phys. 11, 2329–2340 (1970)
D.M. Greenberger, Theory of particles with variable mass. II. Some physical consequences. J. Math. Phys. 11, 2341–2347 (1970)
S. Kudaka, S. Matsumoto, Uncertainty principle for proper time and mass. J. Math. Phys. 40, 1237–1245 (1999)
I.I. Shapiro, Fourth test of general relativity. Phys. Rev. Lett. 13, 789–791 (1964)
N.D. Birrell, P.C.W. Davies, Quantum Fields in Curved Space, no. 7 (Cambridge university press, 1984)
K. Tanaka, How to detect the gravitationally induced phase shift of electromagnetic waves by optical-fiber interferometry. Phys. Rev. Lett. 51, 378 (1983)
H. HŘbel, M. R. Vanner, T. Lederer, B. Blauensteiner, T. LorŘnser, A. Poppe, A. Zeilinger, High-fidelity transmission of polarization encoded qubits from an entangled source over 100 km of fiber. Opt. Express 15, 7853–7862 (2007)
P.J. Mosley, J.S. Lundeen, B.J. Smith, P. Wasylczyk, A.B. U’Ren, C. Silberhorn, I.A. Walmsley, Heralded generation of ultrafast single photons in pure quantum states. Phys. Rev. Lett. 100, 133601 (2008)
G. Sansone, L. Poletto, M. Nisoli, High-energy attosecond light sources. Nat. Photonics 5, 655–663 (2011)
L. Gallmann, C. Cirelli, U. Keller, Attosecond science: recent highlights and future trends. Ann. Rev. Phys. Chem. 63, 447–469 (2012)
N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, K. Edamatsu, Observation of optical-fibre Kerr nonlinearity at the single-photon level. Nat. Photonics 3, 95–98 (2009)
G.-Y. Xiang, B.L. Higgins, D. Berry, H.M. Wiseman, G. Pryde, Entanglement-enhanced measurement of a completely unknown optical phase. Nat. Photonics 5, 43–47 (2011)
R. Ghosh, C. Hong, Z. Ou, L. Mandel, Interference of two photons in parametric down conversion. Phys. Rev. A 34, 3962 (1986)
T. Ralph, G. Milburn, T. Downes, Quantum connectivity of space-time and gravitationally induced decorrelation of entanglement. Phys. Rev. A 79, 022121 (2009)
J. Franson, Bell inequality for position and time. Phys. Rev. Lett. 62, 2205 (1989)
S. Aerts, P. Kwiat, J.-A. Larsson, M. Zukowski, Two-photon Franson-type experiments and local realism. Phys. Rev. Lett. 83, 2872 (1999)
R. Pound, G. Rebka, Apparent weight of photons. Phys. Rev. Lett. 4, 337–341 (1960)
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Zych, M. (2017). Interference of “Clocks”—Experimental Proposals. In: Quantum Systems under Gravitational Time Dilation. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-53192-2_5
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