Testing de Broglie-Bohm Theorywith 21st Century Technology

Peter J. RiggsAustralian National University

21st-century directions in de Broglie-Bohm theory and beyondInternational Quantum Foundations Workshop

Saturday 28th August - Saturday 4th September 2010The Apuan Alps Centre for Physics

Vallico Sotto, Tuscany

• The biggest advance for the de Broglie-Bohm Theory would be to demonstrate an empirical superiority over Orthodox Quantum Theory.

• This presentation outlines how 21st Century technology might provide one means to do this.

• Technical details may be found in the references cited at the end of the presentation.

Introduction

We are all familiar with the case of a spinless particle confined to a force-free region of space (a box or well).

Particle in a BoxParticle in a Box

The particle is confined by setting V = outside the box and V = 0 inside the box.

In one dimension, the wavefunction in the box has the simple form:ψn(x) = (2/L)½ sin (nπx/L) with energy En = n2 h2/(8mL2)

where L is the box length, h is Planck’s Constant, m is the particle’s inertial mass, and n is a positive integer.

V =

0 L x

V = V = 0

The wave field (matter wave) for the lowest energy state in an infinite square well.

Particle in a Box - VisualisationParticle in a Box - Visualisation

• In Orthodox Quantum Theory (OQT), the particle in the box is always in motion (or this would violate the Uncertainty Principle as understood in OQT).

• In three dimensions, the wavefunction in a cubical box is:

ψ = (2/L)3/2sin(n1x/L) sin(n2y/L) sin(n3z/L)e-iEnt/ћ = Re-iS/ћ

• In de Broglie-Bohm Theory, the momentum is: p = S (for a spinless particle). Since S = – Ent, S = 0

the particle is at rest.

• Can we test these different theoretical predictions?

Particle in a BoxParticle in a Box

Measurement of particle attributes inside box

Standard methods of measurement:

- open box and ‘have a look’;

- use a probe, e.g. scattered light waves.

The standard methods all fail due to disturbances to particle.

• Does 21st Century technology provide any new method to test the different predictions?Note that only trying to find if the particle is in

motion.Need to have a measurement that does not disturb

the particle.• The answer is:

Yes! 21st Century laser technology and atom optics provides a suitable method of measurement.

Measurement of particle attributes inside box

Evanescent Waves• Evanescent waves are

electromagnetic waves that penetrate tens of nanometers through a surface and propagate along the surface.

• They penetrate a small distance into the medium and decay exponentially in the transverse direction.

• Energy is transferred along the boundary.

For angle θ > critical angle and

refractive index n1 > n2 , total

internal reflection occurs and

gives rise to an evanescent wave.

Evanescent wavepropagation

directionn2

n1θ

Laser Cooling of Atoms

• Only laser light with the correct frequency is absorbed by an atom.

• Atoms accelerate or decelerate when absorbing laser light.

• Atoms can now be trapped and cooled to milli-Kelvin temperatures or less.

• At these temperatures, wave nature of atoms dominates.

The Proposed Experimental Set-up:A cold atom placed in a specially designed atom trap

• A ‘blue-detuned’ laser beam undergoing total internal reflection is used to create a evanescent wave.

• The ‘mirror’ for a cold atom is an evanescent wave at the surface of the (inside) end of a containment vessel.

• Evanescent waves generated at both ends by laser beams produce an effectively infinite well.

Laser beamLaser beam

Evanescent wave Evanescent wave

Containment vessel (atom trap)

cold atom

• A single atom (with zero spin) is ‘cooled’ to lower its speed so that reflection by an evanescent light wave can occur and so that its thermal de Broglie wavelength is of the order of the box dimensions.

• The atom is placed in the containment vessel and then the optical forces used to hold the atom are turned off.

• The lasers used to produce the evanescent waves are concurrently switched on.

The Experimental Method: Single Atom Reflection from an Evanescent-wave ‘Mirror’

• In being elastically reflected by the evanescent wave, the atom will not absorb energy but will cause a small phase shift in the reflected laser beam.

• This phase shift will be proportional to the change in momentum of the atom on its reflection.

• A measurement of any resulting phase shift would then determine if the atom is in motion

– a non-destructive measurement!

The Experimental Method: Single Atom Reflection from an Evanescent-wave ‘Mirror’

• If the Orthodox Quantum Theory prediction is correct, then a phase shift in the laser light which corresponds to the kinetic energy of the trapped atom will be found.

• If the de Broglie-Bohm Theory prediction is correct, one would expect (in an ideal situation) no phase shift at all.

Testing the Prediction of de Broglie-Bohm Theory: Single Atom Reflection from an Evanescent-wave ‘Mirror’

• If the wave field is accepted as physically real then zero phase shift result would depend on whether the wave field itself remains undisturbed by the evanescent waves.

• If such a disturbance could not be avoided in practice, or made ineffective, then a phase shift that indicates momentum smaller than predicted by Orthodox Quantum Theory would also constitute confirmation of the de Broglie-Bohm Theory prediction.

Testing the Prediction of de Broglie-Bohm Theory: Single Atom Reflection from an Evanescent-wave ‘Mirror’

Quantum Reflection of a Cold Atom

• The experiment described for a single atom would be very difficult to conduct but is certainly possible.

• The challenge is for experimentalists to design a feasible version and put it to the test.

• The use of an evanescent wave as a quantum ‘mirror’ for a cold atom need not be the only way to perform this test.

• If in doubt, take heed of the recent history of ultra-cold physics and be cautious in stating what experimentalists cannot achieve!

Thank-you !

Any questions?

References

1. Riggs, P.J. 2009. Quantum Causality: Conceptual Issues in the Causal Theory of Quantum Mechanics (Dordrecht: Springer).

2. Courtois, J.-Y. et al. 1995. 'Quantum nondemolition measurements using a crossed Kerr effect between atomic and light fields', Physical Review A 52: 1507-1517.

3. Dowling, J.P. and Gea-Banacloche, J. 1995. 'Schrödinger modal structure of cubical, pyramidal, and conical, evanescent light-wave gravitational atom traps', Physical Review A 52: 3997–4003.

4. Aspect, A. et al. 1995. 'Nondestructive Detection of Atoms Bouncing on an Evanescent Wave', Physical Review A 52: 4704-4708.

5. Shimizu, S. et al. 2004. 'Design of atomic mirror for silicon atoms', Science and Technology of Advanced Materials 5: 581-583.

6. Kallush, S. et al. 2005. 'Manipulating atoms and molecules with evanescent-wave mirrors', European Physical Journal D 35: 3-14.

7. http://commons.wikimedia.org/wiki/File:2D_Wavefunction_(1,1)_Surface_Plot.png

Possible Questions1) Has any part of the proposed test been experimentally

verified?Yes. The trapping and ‘cooling’ of atoms to the speeds required and their reflection by evanescent light waves have been achieved.

2) How can a measurement of any resulting phase shift be performed?This is done by interferring the reflected laser beam with a reference laser beam of known phase.

3) Does the Quantum Equilibrium Condition, P(x) = ψ2, affect the validity of the proposed measurement?No. The limitation due to P(x) = ψ2 applies to standard measurements. Since this is a non-destructive measurement of one parameter (change in momentum) of a single atom only, Quantum Equilibrium does not affect the result.