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Научни трудове на Съюза на учените в България-Пловдив. Серия В. Техника и технологии, естествен ии хуманитарни науки, том XVI., Съюз на учените сесия "Международна конференция на младите учени" 13-15 юни 2013. Scientific research of the Union of Scientists in Bulgaria-Plovdiv, series C. Natural Sciences and Humanities, Vol. XVI, ISSN 1311-9192, Union of Scientists, International Conference of Young Scientists, 13 - 15 June 2013, Plovdiv.
THE NON-LOCAL NATURE OF QUANTUM MECHANICS: A STUDENT LABORATORY EXPERIMENT
Edward morvan Benhaim, Victor Lebedev, and Antoine weis University of Fribourg, Physics Department, Ch. du musée 3, CH-1700
Fribourg, Switzerland e-mail: [email protected] e-mail: [email protected] e-mail: [email protected]
Abstract
Classical physics assumes that the world is real, in the sense that objects have certain properties and positions, independently from the observer. It is also assumed that identical causes always produce the same effect. In this sense nature is assumed to be deterministic, and everything is well defined. Classical physics also generally assumes that a certain action on an object at one place in the universe cannot affect an object at the other side of the universe, without the objects being linked by chain of causal relations which propagate at some speed strictly less or equal to c, the speed of light. In this sense the laws of nature are also assumed to be local. The concept of reality has been questioned by the quantum description of nature. Quantum mechanics (QM) claims that quantum objects (i.e., the constituents of the world surrounding us) do not have defined a priori properties. QM moreover predicts the existence of so called entangled states that have no counter-part in classical physics. In its simplest form an entangled system consists of two subsystems that cannot be described mathematically as two disjoint systems. As a consequence, a perturbation on one sub-system will influence the other sub-system simultaneously, no matter the distance between them. Here we describe a student laboratory experiment on entangled photon pairs that demonstrates unambiguously the existence of non-local systems in nature.
1. Introduction
In classical physics, the properties of a physical system — such as the position and velocity of each particle in an ensemble — have a fixed value at each instant (Fig. 1). Repeating a given measurement on identical copies of the system, will always yield the same result, a fact known as determinism.
Fig. 1: Classical description of physical systems: all properties are well defined.
A system property at position Xj will not influence the outcome of a measurement made simultaneously at position x2, a property called locality. Classical physics is thus deterministic and local.
Quantum mechanics assumes that the properties of a physical system are not defined until the instant of their measurement. QM is thus non-deterministic and one can make only probabilistic predictions about the result of a measurements. A quantum system is described by a mathematical object, the wave function, whose square represents a probability (Fig. 2.a,b) to find a given value of its properties (position, velocity, angular momentum, etc). In addition, QM predicts the existence of so-called entangled states which have no counter-part in classical physics [1]. The simplest entangled state is formed by two identical particles, which have the same common origin (Fig. 2.c). The two particles may be very far apart, but they are still described by one single wave function. As a consequence, a measurement of a given property of one of the particles will instantaneously affect the same property of the partner particle. This "spooky action at a distance" (Einstein) makes QM non-local [2].
a)
b)
c)
Fig. 2: Quantum description of physical systems: a) single particle, one wave function; b) two independent particles, two separated wave functions; c) entangled state formed by two correlated particle, sharing one wave functions. The particle properties are described by probability clouds defined as the square of the system's wave function. Here the clouds represent the probabilities to find the quantum object at a certain position in space.
Here we describe an advanced student laboratory experiment which allows the discrimination between the classical and quantum nature of physical reality. The experiments are performed on pairs of entangled infrared photons produced by nonlinear crystals. The apparatus is a reproduction of the arrangement described in [3,4].
2. Understanding the experiment a) Parametric down-conversion
A type 1 down-converting crystal creates two identical low energy (infrared, D=810 nm in our experiment) from one energetic photon, here blue light at 405 nm (Fig. 3). The efficiency of the process is maximal when the polarization of the incoming photon is perpendicular to the
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crystal axis. The polarizations of the two outgoing photons are parallel to the crystal axis.
Fig. 3: Optical scheme of the parametric down-conversion process. A 405 nm laser beam incident on the crystal produces outgoing 810 nm wavelength photon pairs moving along symmetric trajectories on a cone. The polarizations of the outgoing photons are parallel to the crystal axis.
b) State superposition
Using two crystals with mutually perpendicular optical axes (Fig. 4), the down-conversion produces outgoing photon pairs in polarization superposition states. By choosing the input polarization of 45° with respect to the crystal axes, photons with horizontal and vertical polarization are produced with the same probability.
Fig. 4: Putting two down-converting crystals together. The V and the H stand for vertically and horizontally polarized light.
Since one does not know which crystal has produced the pair, each of the two correlated photons is simultaneously horizontally and vertically polarized.
c) Polarization correlations
Two photon counters A and B are placed at diametrically opposite positions on the photon emission cone. Prior to their detection each photon has to pass a linear polarizer placed in front of the detector. The two polarizers can be oriented at arbitrary angles □ and □, respectively, with respect to the horizontal (plane of the optical table). The pulses from the two photon counters are sent to a coincidence unit (not shown), which is used to count the correlated counts, i.e., the simultaneous detection of photons by the two detectors during a certain amount of time.
Fig. 5: Experimental setup (top view).
We denote by P(UU) the probability that the detectors fire simultaneously when their polarizers are oriented at □ and □, respectively. In the experiment P(U U) denotes the number of coincidence counts registered during a given time interval.
d) Classical and quantum description of the photons pairs
The difference between the classical and quantum descriptions can be appreciated by comparing their respective predictions for the rates P(UU) of correlated counts for different polarizer orientations.
In classical terms the ensemble of photon pairs can be viewed as a collection of 50% fully vertically polarized pairs and 50% fully horizontally polarized pairs. The probability is then given by:
=
1 + cos(2ct) cos(2|3)
(1)
Using the probabilistic quantum description of entangled states yields a probability:
(2)
Following the suggestion of Bell [5] we combine the probabilities into a function E(U, □ , defined as:
E{a,fi) = P{cc,0) + P(_a + 90°,jff + 90°) — P(_a + 90°,- P(cc,p + 9QD)
(3)
Comparing the measurement results for different sets of angles (□.□□'□ □ n.'andn '. □ '. one can form a quantity S, defined as:
This function can be simplified by choosing □□□□'□'□□' □"□and □ □ '=3 □which leads to the following predictions (shown in Fig. 5) for the dependence S(Q
Classical Physics Quantum Mechanics
5(0) = 21 S(<P) = 2 land
Fig. 5: Graphical representation of the S(U The solid (blue) curve represents the expectation based on classical physics and the red (dotted) curve the quantum result. The horizontal black line shows our result with the experimental error range indicated by dashed lines.
The experimental measurement of S thus allows us to make a clear distinction between the classical and quantum descriptions of the system.
3. Experiments and results
All mechanical and optical components as well as the light source (405 nm diode laser, TCLDM9, 15 mW) used to build the experiment are stock items from Thorlabs. The crystal is a □ -barium borate crystal (walk-off angle of 2.7° for type-1 1064 SHG) from Dohrer Elektrooptik. The photon counting modules (SPCM-AQRH-13-FC) use an unique silicon avalanche photodiode, from Perkin Elmer. The ensemble is mounted on a granite optical table for stability.
Using □= -45°, □= -22.5°, □'= 0° and □'= 22.5°, we obtained:
5 = 2.41 = 0.08
(5)
which shows that the classical description of the polarization correlated photon pairs is unacceptable.
4. Summary
We have presented a student laboratory experiment designed to show that the classical description and quantum description of nature are in contradiction. One is forced to accept that the quantum formalism is valid and that quantum objects have non-local properties.
References
Bell, J., "On the Einstein Podolsky Rosen Paradox", Physics 1 (1964) 195.
Einstein, A.; Podolsky, B.; Rosen, N., "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?", Phys. Rev. 47 (1935) 777.
Dehlinger, D. ; Mitchell, M. W. , "Entangled photons, nonlocality, and Bell inequalities in the undergraduate laboratory". Am. J. Phys. 70 (2002) 903.
Dehlinger, D. ; Mitchell, M. W. , "Entangled photon apparatus for the undergraduate laboratory'. Am. J. Phys. 70 (2002) 898.
Bell, J., "Speakable and unspeakable in quantum mechanics " University Press Cambridge (1984).
