Single electron relativistic clock interferometer

P. Bushev (20051517), Jared H. Cole, D Sholokhov (20051520), N Kukharchyk (20051523), Magdelena Zych (20051526)

Published Nov 2, 2024• 21 citations

Abstract

Although time is one of the fundamental notions in physics, it does not have a unique description. In quantum theory time is a parameter ordering the succession of the probability amplitudes of a quantum system, while according to relativity theory each system experiences in general a different proper time, depending on the system's world line, due to time dilation. It is therefore of fundamental interest to test the notion of time in the regime where both quantum and relativistic effects play a role, for example, when different amplitudes of a single quantum clock experience different magnitudes of time dilation. Here we propose a realization of such an experiment with a single electron in a Penning trap. The clock can be implemented in the electronic spin precession and its time dilation then depends on the radial (cyclotron) state of the electron. We show that coherent manipulation and detection of the electron can be achieved already with present day technology. A single electron in a Penning trap is a technologically ready platform where the notion of time can be probed in a hitherto untested regime, where it requires a relativistic as well as quantum description.

Related papers

Single electron relativistic clock interferometer

P A Bushev, Jared H. Cole, D Sholokhov +2 more

Although time is one of the fundamental notions in physics, it does not have a unique description.In quantum theory time is a parameter ordering the succession of the probability amplitudes of a quantum system, while according to relativity theory each system experiences in general a different proper time, depending on the systemʼs world line, due to time dilation.It is therefore of fundamental interest to test the notion of time in the regime where both quantum and relativistic effects play a role, for example, when different amplitudes of a single quantum clock experience different magnitudes of time dilation.Here we propose a realization of such an experiment with a single electron in a Penning trap.The clock can be implemented in the electronic spin precession and its time dilation then depends on the radial (cyclotron) state of the electron.We show that coherent manipulation and detection of the electron can be achieved already with present day technology.A single electron in a Penning trap is a technologically ready platform where the notion of time can be probed in a hitherto untested regime, where it requires a relativistic as well as quantum description.

arXiv:1604.06217New Journal of PhysicsSep 27, 201625 citations

General relativistic effects in quantum interference of “clocks”

Magdalena Zych, Igor Pikovski, Fabio Costa +1 more

Quantum mechanics and general relativity have been each successfully tested in numerous experiments. However, the regime where both theories are jointly required to explain physical phenomena remains untested by laboratory experiments, and is also not fully understood by theory. This contribution reviews recent ideas for a new type of experiments: quantum interference of "clocks", which aim to test novel quantum effects that arise from time dilation. "Clock" interference experiments could be realised with atoms or photons in near future laboratory experiments.

arXiv:1607.04022Journal of Physics Conference SeriesJun 1, 201631 citations

Quantum Signatures of Proper Time in Optical Ion Clocks

Gabriel Sorci, Joshua Foo, Dietrich G. Leibfried +2 more

Optical clocks based on atoms and ions probe relativistic effects with unprecedented sensitivity. They resolve time dilation due to atom motion or different positions in the gravitational potential through frequency shifts. However, all measurements of time dilation so far can be explained effectively as the result of dynamics with respect to a classical proper time parameter. Here we show that atomic clocks can probe effects where a classical description of the proper time dynamics is insufficient as superpositions of proper time emerge. We apply a Hamiltonian formalism to derive time dilation effects in harmonically trapped clock atoms and show how second-order Doppler shifts due to the vacuum energy, squeezing, and quantum corrections to the dynamics arise. We also demonstrate that time-dilation-induced entanglement between motion and clock evolution can become observable in state-of-the-art clocks when the motion of the atoms is strongly squeezed, realizing proper time interferometry. Our results show that experiments with trapped ion clocks are within reach of probing relativistic evolution of clocks for which a quantum description of proper time becomes necessary.

arXiv:2509.09573Physical Review LettersFeb 27, 20263 citations

Entanglement of quantum clocks through gravity

Esteban Castro-Ruiz, Flaminia Giacomini, Časlav Brukner

In general relativity, the picture of space-time assigns an ideal clock to each world line. Being ideal, gravitational effects due to these clocks are ignored and the flow of time according to one clock is not affected by the presence of clocks along nearby world lines. However, if time is defined operationally, as a pointer position of a physical clock that obeys the principles of general relativity and quantum mechanics, such a picture is, at most, a convenient fiction. Specifically, we show that the general relativistic mass-energy equivalence implies gravitational interaction between the clocks, whereas the quantum mechanical superposition of energy eigenstates leads to a nonfixed metric background. Based only on the assumption that both principles hold in this situation, we show that the clocks necessarily get entangled through time dilation effect, which eventually leads to a loss of coherence of a single clock. Hence, the time as measured by a single clock is not well defined. However, the general relativistic notion of time is recovered in the classical limit of clocks.

arXiv:1507.01955Proceedings of the National Academy of SciencesMar 7, 201774 citations

Measuring time with physical clocks

Esteban Castro-Ruiz, Flaminia Giacomini, Časlav Brukner

In general relativity, the picture of spacetime assigns an ideal clock to each spacetime point. Being ideal, gravitational effects due to these clocks are ignored and the flow of time according to one clock is not affected by the presence of surrounding clocks. However, if time is defined operationally, as a pointer position of a physical clock that obeys the laws of quantum mechanics and general relativity, such a picture is at most a convenient fiction. We show that the mass-energy equivalence implies gravitational interaction between the clocks, while the superposition of energy eigenstates leads to a non-fixed metric background. Based only on the assumption that both quantum mechanics and general relativity are valid in this situation, we show that the clocks necessarily get entangled through time dilation effect, which eventually leads to a loss of coherence of a single clock. Hence, the time as measured by a single clock is not well-defined. However, the general relativistic notion of time is recovered in the classical limit of clocks.

Jul 7, 20151 citation

Interference of clocks: A quantum twin paradox

Sina Loriani, Alexander Friedrich, Christian Ufrecht +15 more

The phase of matter waves depends on proper time and is therefore susceptible to special-relativistic (kinematic) and gravitational (redshift) time dilation. Hence, it is conceivable that atom interferometers measure general-relativistic time-dilation effects. In contrast to this intuition, we show that (i) closed light-pulse interferometers without clock transitions during the pulse sequence are not sensitive to gravitational time dilation in a linear potential. (ii) They can constitute a quantum version of the special-relativistic twin paradox. (iii) Our proposed experimental geometry for a quantum-clock interferometer isolates this effect.

arXiv:1905.09102Science AdvancesOct 4, 201956 citations