All previous experimental tests of Bell inequalities have required additional assumptions. The strong Bell inequalities (i.e. those requiring no additional assumptions) have never been tested. An experiment has been designed that can, for the first time, provide a definitive test of the strong Bell inequalities. Not only will the detector efficiency loophole be closed; but the locality condition will also be rigorously enforced. The experiment involves producing two Hg-199 atoms by a resonant Raman dissociation of a mercury dimer ((199)Hg2) that is in an electronic and nuclear spin singlet state. Bell inequalities can be tested by measuring angular momentum correlations between the spin one-half nuclei of the two Hg-199 atoms. The method used to make these latter measurements will be described

Fry, Edward S.

English

NASA Technical Reports Server

N95- 13966
THE STRONG BELL INEQUALITIES
A PROPOSED EXPERIMENTAL TEST
Edward S. Fry
Physics Department, Texas A&M University
College Station, TX 77843
ttlmtract
All previous experimental tests of Bell inequalities have required additional assumptions.
The strong Bell inequalities (i.e. those requiring no additional assumptions) have never been
tested. An experiment has been designed that can, for the first time, provide a definitive test
of the strong Bell inequalities. Not only will the detector efficiency loophole be closed; but,
the locality condition will also be rigorously enforced. The experiment involves producing
two 199Hg atoms by a resonant Raman dissociation of a mercury dimer (199Hg2) that is in an
electromc" and nuclear spin singlet state. Bell inequalities can be tested bY_199measuringangular
momentum correlations between the spin one-half nuclei of the two Hg atoms. The
method used to make these latter measurements will be described.
1 Introduction
Due to low detector efficiencies, previous experimental tests of Bell inequalities have required an
auxiliary assumption in order to derive an experimentally testable inequality. [1"5l A new experimental
concept has been developed that makes it possible to test the strong Bell inequalities (Bell inequalities
without any auxiliary assumptions). It also leads directly to an extension that rigorously enforces
locality.
This approach is an ex_rimental realization of Bohm's version of the Einstein-Podolsky-Rosen
Gedankenexperiment. [3' "J Instead of photon pairs, it involves measurements of the correlations
between angular momentum components of two atoms (actually spin one-half nuclei) of the isotope
199Hg. A brief description of the proposed experiment was recently published, [7] and a very detailed
discussion has also been provided.[81
In general, the measurement of components of spin suggests the use of Stern-Gerlach magnets. For
spin one-half particles, there are two possible projections, + ("spin-up") and - ("spin-down"), of the
spin on the axes of the magnets. As indicated in Figure l, the magnetic field gradient deflects each spin
one-half particle into one of two detectors depending on the projection of its spin on the magnet axis. To
measure a spin component of a particle in any specified direction, one simply rotates the axis of the
corresponding magnet to that direction. However, such an approach is unsuitable in the present work
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for two reasons. First, to enforce Einstein locality, it would be necessary to rotate a magnet to an
arbitrary direction in a time short compared to the time it takes light to travel from one magnet to the other
- a few nanoseconds. This appears to be physically impossible. Second, based on available magnetic
fields and the magnitude of the nuclear magnetic moment, the deflection produced by 199Hg nuclear
spins is so small as to preclude this approach.
Magnet axis _ •l Z _ Magnet axis
y Ii ,
"Spin-up" ! _ _ _ ]_ "Spin-up"
C_,----_ __ _I"_ -gl s 2 _ . _1-'-a
Detectors -_ '["- D-- _r
] [-_,[_t--_-- _.____ _ _1. eteet_s
r---b  our e I ..... -=-"
Spin-down" L'---_ ! I S=O _ bpm-aown
Stem-Gerlach Stern-Gerlach
Analyzer Analyzer
FIG. 1. Schematic of a Stern-Gerlach apparatus for measuring spin correlations. The
diagram assumes spin one-half particles and the magnets are oriented for measurements of
the spin components of both particles in the Z direction.
Other approaches to the measurement of spin components are possible. For example, a Bell
inequality involving _roton spin correlations has been tested using proton-proton scattering to determine
the spin components. [9] However, this type of approach requires several auxiliary assumptions.
Efficient detection of atoms is combined with spin analysis in the approach to be described here.
This approach takes advantage of the hyperfine structure interaction in 199Hg atoms in order to select
nuclear spin components via electric dipole transitions. Detection efficiency is sufficiently high to close
that loophole. And finally, this approach permits a very rapid change in the direction of the measurement
of spin components; hence Einstein locality can be enforced.
2 Overview of the Proposed Experiment
The 199Hg atoms are produced by a stimulated Raman excitation to a dissociating state of the XIY-_
ground state of a 199Hg dimer. The total electron and the total nuclear spin angular momenta are both
zero in the initial rotational state of the Hg dimers, and are not changed in the dissociation process. The
two mercury atoms resulting from the dissociation are both in IS 0 ground states. Since the electronic
576
angular momentum is J=0 and the nuclear spin of 199I-Ig is I=1/2, each ground state atom therefore has a
total angular momentum F=l/2. The component of total angular momentum (which is therefore the
component of nuclear spin) in any given direction is measured by orienting excitation laser beams at
253.7 nm in that direction and using polarization selective excitation of one of the Zeeman sublevels.
For left circularly polarized excitation, only atoms whose component of angular momentum, MF=+I/2,
in the direction of laser beam propagation are excited. Similarly, right circularly polarized light only
excites atoms with MF-=-1/2. Excited atoms are photoionized via an auto-ionizing state using a laser at
197.3 nm. The resulting photoelectrons and ions are detected using Channeltron electron multipliers.
Assuming a mercury atom has been detected if EITHER an electron OR an ion is observed, then the
overall detection efficiency for the Hg atoms is greater than 96%. Figure 2 shows a schematic of the
experiment indicating the relative directions of the dimer, atom, and laser beams.
Dimer Excitation Z
Laser Beam: 266 nm _
Dimer Dissociating
Laser Beam: 355 nm
Hg 2 (Dlmer)
Ionizing
Laser
Beam:
197.3 nm
01
Ionizing Laser
Beam: 197.3 nm
Hg atom
Hg atom
X
Analyzing Laser
Beam: 253.7 nm
Analyzing Laser
Beam: 253.7 nm
FIG. 2. Schematic of the experiment showing the direction of the mercury dimer beam
together with a pair of the dissociated atoms and their respective detection planes. Relative
directions of the various laser beams are also shown.
Rates for simultaneous detection (coincidence rates) of the two atoms are measured for components
of their angular momenta in the directions 01 and 02, respectively (i. e. in the directions of the
excitation laser beams). A set of four angles can be chosen that give a maximum violation of the strong
Bell inequality. [7' 8] This experiment also lays the foundation for an experiment that enforces locality
577
since a combination of a Pockels cell and a beamsplitting polarizer can be used to stochastically change
the direction of the exciting laser beams on the nanosecond time scale.
3 Measurement of the Nuclear Spin Components
Figure 3 shows the relevant energy levels of the mercury atom, [10] and the corresponding transitions
at 253.7 nm for spin analysis and at 197.3 nm for detection via photo ionization. The first transition is
from the (6s2)61S0 (F = Y2) ground state (level 1)to the (6s6p)63P1 (F = _2) state (level 2); the
second transition is from level 2 to the (6p2)3po autoionizing state (level 3). Atom detection is via both
the resulting ion and the photoelectron.
Assuming a Fano profile for the autoionizing transition, a calculated value for its oscillator strength,
and a measured value for its width, a theoretical value of --2.3x10 "14 cm 2 is obtained for the peak cross-
section.J7, 8] This is an unusually large cross-section, but is consistent with measured cross-sections for
analogous transitions in Cd. [11] Since both transitions are so strong, laser pulse energies of only 60 I.tJ
and 250 }.tJ, respectively, are sufficient to ionize all the atoms in a few nanoseconds.
Level 2 (6s6p) 63PI
(125 nsec)
197.3 nm
22 GHz
F=3/2
F=1/2t
253.7 nm
Level 1 (6s 2} 6 IS 0 F=1/2
FIG. 3. Relevant energy levels of the mercury atom, [10] and the corresponding transitions
for detection.
As shown in Figure 2, the laser beams for spin analysis have a wavelength of 253.7 nm and lie in
planes perpendicular to the direction to the source. They are at angles 01, 02 to the +Z-axis. The angles
01, 02 of these laser beams define the directions in which each atom's angular momentum components
is observed.
If we choose some arbitrary direction as the quantum axis for our system, then the quantum numbers
for the two components of angular momentum in that directioa are MF=!-_I/2 (for an F=l/2 ground state
578
199Hg atom). If the 253.7 nm laser beam is propagating in the direction of the quantum axis and has
fight circular polarization (if+), then MF must increase by one in the transition. Thus, only ground state
atoms for which the projection of the angular momentum in the direction of laser beam propagation is
3 °
MF=-I/2 can be excited to the 6 P1 (F = Y2) state and ionized; see Figure 4. Similarly, for left
circular polarization, only atoms with MF=+I/2 are excited and ionized. In summary, by choosing an
arbitrary direction and using a circularly polarized excitation laser, a Hg atom with either component of
angular momentum in that direction can be selectively detected.
__!_i_i_:_:_!_iI_I_I_i_i_ii_ I _ _ ! _ i l/_/_ _ i_lt//_li//_ _ _!_/_t_l
"''''''":':_?"',s: ...... "._i:_'".'._.'!.)..ii_i _ .................. :::::::::::::::::::::::::::::::::'ii_iiiiii').'iiii__: :: :: _ ' _ :: :: " "'::"_:'_:_::'::'q_'::_::_':_:" _ _
22 GHz
{6stp) 6 3p; _ F=3/2I/2
(6S 2} 6 1S O /U+ F= 1/2
t ? ? t
M F = -3/2 -1/2 +1/2 +3/2
FIG. 4. Analysis scheme with right circularly polarized light. Since MF must increase by 1
3,,o
in the transition, only ground state atoms with MF=-I/2 can reach the 6 P1 (F = Y2) state.
4 Summary
The use of electric dipole transitions to measure the component of nuclear spin of 199Hg in an
arbitrary direction has been described. Its application to a definitive experimental test of the previously
untested strong Bell inequalities is discussed. This novel approach makes it feasible to rigorously
enforce Einstein locality.
5 Acknowledgement
This research was supported by the Robert A. Welch Foundation grant No. A-1218 and by the
National Science Foundation grant PHY-9221038. The author also thanks Dr. Shifang Li for many
helpful discussions and suggestions.
579
6 References
[81
[91
[101
[1] C.O. Alley and Y. H. Shih, in Proc. 2nd Int. Symp. Foundations of Quantum Mechanics, 47
(Tokyo, 1987).
[2] A. Aspect, J. Dalibard, and G. Roger, Phys. Rev. Lett. 49, 1804 (1982).
I3] J.F. Clauser and A. Shimony, Rep. Prog. Phys. 41, 1881 (1978).
[4] Z.Y. Ou and L. Mandel, Phys. Rev. Lett. 61, 50 (1988).
[5] J.G. Rarity and P. R. Tapster, Phys. Rev. Lett. 64, 2495 (1990).
[6] D. Bohm, Quantum Theory, (Constable, London, England, 1954).
[7] E.S. Fry, in Proceedings of the International Conference on Lasers '92, 621 (Houston, TX,
1993).
E. S. Fry, submitted to Phys. Rev. A (1994).
M. Lamehi-Rachti and W. Mittig, Phys. Rev. D 14, 2543 (1976).
C. E. Moore, Atomic Energy Levels, Volume III, Circular 467 (National Bureau of Standards,
Washington, DC, 1958).
[11] K. Miyazaki, T. Watanabe, and K. Fukuda, J. Phys. Soc. Japan 40, 233 (1976).
58O


The strong Bell inequalities: A proposed experimental test

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