Can gravity affect quantum systems? Quantum theory and
gravity seem to apply to very different physical regimes. It is often argued
that gravity is irrelevant on very small scales, where typical quantum phenomena
are observed. But as has been shown in numerous experiments, gravity can indeed
influence a quantum wave function of the smallest particles. Newtonian gravity
from Earth can induce a quantum phase-shift for a particle that is in a
superposition between two different heights. This was first demonstrated with
Neutrons in the famous COW (Colella-Overhauser-Werner) experiment in 1975 [1].
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The gravitational field causes time dilation: clocks closer to
Earth run slower than clocks further away. For a quantum
superposition of a single clock at two heights, the clock
states and its position become entangled.
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What about Einstein’s gravity? If the Newtonian potential
can influence a quantum wave function, what can one expect from post-Newtonian
effects stemming from general relativity? It turns out that novel phenomena
arise, with no classical analogue. Classically, two clocks placed at different heights will experience different
proper times, and thus will be time dilated with respect to each other. But in
quantum theory, an additional effect arises: If a single clock is brought into
superposition of two heights, its internal degrees of freedom (or clock states)
get entangled with its position [2]. The acquired “which-way information”
affects the quantum coherence of the position.
In a recent publication [3], we showed that the effect of
time dilation on quantum systems is very general and affects the quantum
coherence of any composite quantum system. Time dilation is universal: it
affects any system regardless of its structure or composition. Clocks are
affected by time dilation as much as the heart beat or the half-life of a
decaying particle. In fact, all composite quantum systems are affected, as they
usually have a finite temperature or energy spread: there is usually some internal
dynamics present within the system. If such a composite system is brought into
superposition between different heights above Earth, as in the above example
with a clock, time dilation will correlate all internal dynamics with the
height of the system. And this causes decoherence of the center-of-mass if a sufficient difference in proper times is accumulated along the superposed paths. Quantum coherence is lost because of the relative time delay of the internal dynamics of the system, which becomes position-dependent due to gravitational time dilation. There is no “external”
environment, only the presence of time dilation causes the system’s
center-of-mass to decohere due to the dynamics of its own composition. The effect follows from two very basic concepts of quantum theory and relativity: time dilation and quantum superpositions.
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A complex molecule in superposition in a gravitational
field. Because of time dilation, the frequencies of the
individual atoms depend on the height of the molecule.
This causes decoherence of quantum superpositions
of the center-of-mass of the molecule.
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Even though time dilation is very weak on Earth, the effect can
already be relevant on mesoscopic scales: If a micro-scale object at room
temperature is put into a micrometer superposition, then time dilation will
cause decoherence on the order of milliseconds. This is because many internal
degrees of freedom contribute to the effect. Each individually is affected by
time dilation only a tiny bit, but for a larger composite system, the effect
can become significant. For quantum systems, it is of course very challenging
to prepare such large superpositions, and other decoherence effects will also
be of importance. But there is a parameter range at superfluid Helium temperatures,
where experiments with very large molecules or microspheres could in principle
observe the predicted phenomena in the future. Importantly, the effect is
universal and any internal dynamics
will contribute to decoherence. Thus one can think of other possible experiments,
utilizing any internal dynamics. Many basic concepts that enter the effect are also discussed in our pedagogical note [4].
Finally, what do we actually learn from this study? In our
work, we do not treat the gravitational field quantum mechanically, thus there
is no direct connection to “quantum gravity”. Yet, we study how quantum
mechanical test systems behave on a background space-time, as opposed to
classical test particles, and new effects arise. We found a new decoherence
mechanism, but the most important aspect of the work is that the interplay
between quantum theory and gravity has novel phenomena to offer. Our work shows
one example, but this research direction is still widely unexplored: Many more
possible effects and experiments on the interplay between these two great
theories are waiting to be discovered!
[1] R. Colella, A.
W. Overhauser, S. A. Werner. “Observation of Gravitationally Induced
Quantum Interference”, Phys. Rev.
Lett. 34, 1472 (1975).
[2] M. Zych, F.
Costa, I. Pikovski, Č. Brukner. “Quantum interferometric visibility as a
witness of general relativistic proper time”, Nature Communications 2,505 (2011).
[3] I. Pikovski, M. Zych, F. Costa, Č. Brukner, “Universal
decoherence due to gravitational time dilation”, Nature Physics 11,668-672 (2015).
[4] I. Pikovski, M. Zych, F. Costa, Č. Brukner, “Time
Dilation in Quantum Systems and Decoherence: Questions and Answers”, arXiv:1508.03296 [quant-ph] (2015).
