Search for Quantum Gravity Using Atom Interferometers

Charles Wang, University of Aberdeen, UK

Robert Bingham, Rutherford Appleton Laboratory, UK

Tito Mendonca, Instituto Superior Tecnico, Portugal

Workshop on Fundamental Physics, Cosener’s House, RAL, 3 – 5 May 2006

HYPER

Atom interferometers and Quantum Gravity

• Grand unification theory (GUT) predict that the four forces of nature unify close to the planck scale.

• Spacetime is smooth on the normal scales but granulated due to quantum gravity on the Planck scale Quantum Foam

Planck time planck G c 3s

Planck length cplanck G c2 35 m

Planck mass Mplanck c/G 10-8 kg

Planck energy 1019 GeV

Planck mass

Workshop on Fundamental Physics, Cosener’s House, RAL, 3 – 5 May 2006

HYPER

Quantum Foam of Spacetime

• Spacetime at the Planck scale could be topologically nontrivial, manifesting a granulated structure Quantum Foam

• Quantum decoherence puts limits on spacetime fluctuations at the Planck scale.

• Semi-classical and Superstring theory support the idea of loss of quantum coherence.

Workshop on Fundamental Physics, Cosener’s House, RAL, 3 – 5 May 2006

HYPER

Atom Interferometers and Quantum Gravity

Produces decoherence in an atom interferometer

• How can an atom interferometer measure physics on the Planck scale?

• Einstein’s (1905) Brownian motion work of inferred properties of atoms by observing stochastic motion of macrostructure’s

• Space time fluctuations on the Planck scale produce stochastic phase shifts.

Diffusion of the wave function.

Workshop on Fundamental Physics, Cosener’s House, RAL, 3 – 5 May 2006

Random walk of a Brownian particle (blue) due to stochastic interactions with molecules (red).

HYPER

Atom Interferometers and Quantum Gravity

Stochastic ProcessQuantum gravity fluctuations stochastic phase shifts

A stochastic process like Brownian

motion is a diffusion process

Regular phase due to smooth spacetime

shift is .

Space time fluctuations regular

phase multiplied by to/.

Results in fluctuating phase

to

[Percival 1997]

Workshop on Fundamental Physics, Cosener’s House, RAL, 3 – 5 May 2006

HYPER

Physics of Decoherence

Difficult to avoid interaction with environment.

Natural Vibrations of the system.Collisions with ambient particles.

Interaction with its own components.

Black body radiation.

Spacetime time quantum fluctuations.

Workshop on Fundamental Physics, Cosener’s House, RAL, 3 – 5 May 2006

HYPER

Previous Estimate of Quantum Gravitational Decoherence

• Granulation of space-time - Universe no longer four dimensional, higher number of dimensions are required. e.g. Superstring theory - 10 dimensions

• Length scale below which granulation is important

• This is an effective cut-off for quantum gravity theories determined by the amplitude of zero point gravitational fluctuations previously estimated to be:

where is the cut-off frequency, and

• From theoretical considerations is in range 102 – 106

planckoffcut

222 planckMo tA

M 7

1

2

42

0/~

TtcM planck

Workshop on Fundamental Physics, Cosener’s House, RAL, 3 – 5 May 2006

HYPER

Previous Estimate of Quantum Gravitational Decoherence

• This implies that experiments using caesium atom interferometers by Peters et al 1997 and fullerene C70 molecule interferometer by Hackermueller et al 2004 set a lower bound of to be of order 10.

• Improvements on experimental sensitivity can raise this value.

• However, the 1/7-th power makes the rise very slow.

Workshop on Fundamental Physics, Cosener’s House, RAL, 3 – 5 May 2006

A fullerene molecule

HYPER

New Estimate of Quantum Gravitational Decoherence

• Previous estimates are based on conformal fluctuations of spacetime. The effects of gravitons (quantized gravitational waves) are ignored.

• Recent developments of conformal decomposition in canonical gravity (Wang 2005: PRD 71, 124026 & PRD 72, 087501) makes it possible to develop a more satisfactory quantum gravitational decoherence model without freezing any degrees of freedom of general relativity.

Workshop on Fundamental Physics, Cosener’s House, RAL, 3 – 5 May 2006

The shearing nature of gravitational waves

Spacetime evolution with diffeomorphism, spin & conformal invariance

HYPER

New Estimate of Quantum Gravitational Decoherence

• The gravitational Hamiltonian in a local laboratory frame can be written as

H = H(CF) +H(GW)

where H(CF) is the negative Hamiltonian of the conformal field and H(GW) is the positive Hamiltonian of the gravitational wave.

• The value of H(CF) depends on time-slicing. In order to avoid huge vacuum energy (so-called cosmological constant problem), the laboratory time-slicing must be chosen so that H(CF) cancels the zero point energy part of H(GW).

• This leads to the new formula (Preprint: Bingham, Mendonca & Wang 2006):

Workshop on Fundamental Physics, Cosener’s House, RAL, 3 – 5 May 2006

3

1

2

42

0/~

TtcM planck

HYPER

New Estimate of Quantum Gravitational Decoherence

• The above-mentioned experiments using caesium atom interferometers by Peters et al 1997 and fullerene C70 molecule interferometer by Hackermueller et al 2004 now yields a lower bound of to be of order 104, well within the accepted range of 102 – 106 .

• It strongly suggests that the measured decoherence effects areconverging towards the fundamental decoherence due to quantumgravity.

Workshop on Fundamental Physics, Cosener’s House, RAL, 3 – 5 May 2006

A fullerene molecule

HYPER

Quantum Limits on Atom Interferometers

• In matter interferometers it is difficult to avoid interactions with the environment and these also suppress the interference.

• The decoherence may be caused by interaction with blackbody radiation, collisions, restraint by a tie down system or even interaction with its own components/atoms.

• Position uncertainty limit is

• The challenge is to detect the spacetime fluctuations unambiguously.

• Future advanced matter wave interferometers will put upper limits to the measurement of decoherence providing tests for the various theories.

Workshop on Fundamental Physics, Cosener’s House, RAL, 3 – 5 May 2006

HYPER

Conclusions

• Theories of quantum gravity support the idea of loss of coherence in matter interferometers.

• In matter interferometers it is difficult to avoid interactions with the environment.

• The challenge is to detect the spacetime fluctuations unambiguously.

• Advanced matter interferometers such as HYPER will put upper limits to the measurement of decoherence providing tests for the various theories of quantum gravity.

• Investigating Planck scale physics using advanced matter interferometers is becoming a reality in the near future.

• The final value of will be a compelling evidence for the quantum behaviour of spacetime and set a stringent benchmark in the search for quantum gravity.

Workshop on Fundamental Physics, Cosener’s House, RAL, 3 – 5 May 2006