|
ScienceWeek
QUANTUM PHYSICS: ON PHOTON ENTANGLEMENT
The following points are made by Dirk Bouwmeester (Nature 2004 429:139):
1) If a double slit is illuminated with a laser beam of wavelength (L) , the familiar rippling pattern of interference fringes arises, even if the attenuation of the laser is so strong that only single photons pass through the double slit at any given instant. To emphasize this quantum feature, Paul Dirac (1902-1984) wrote(1) that "Each photon interferes only with itself. Interference between two different photons never occurs." However, Mitchell et al(2) and Walther et al(3) have reported demonstrations of interference patterns produced by specific entangled states of three and four photons.
2) The resolution in each case is better than it would be for a single photon passing the interferometer: L/3 and L/4 in the three- and four-photon case, respectively, where (L) is the wavelength of an individual photon. Normally, resolution no better than the photon wavelength can be achieved, which is known as the diffraction limit. So, as well as illustrating the properties of multi-particle entanglement, these limit-breaking results are of practical interest -- for high-resolution optical read-out and recording systems, for example, and interferometric position and time measurements.
3) To illustrate how entanglement can be used to produce an interference pattern with a resolution of L/N (where N is the number of entangled particles), consider first the simplest case of N = 2. Two photons are entangled such that they go together through slit A or through slit B of a double-slit configuration. A shorthand notation for this state is (|2A0B + |0A2B) or, even more compact, (|20,02). That this state indeed represents an entangled state follows from the fact that it cannot be written as a product state of two individual photons going through the double slit. The product state would have the additional possibility of one photon going through slit A and the other through slit B. In essence, the two entangled photons form one system, a "bi-photon", if you like, that has twice the energy of a single photon and, therefore, half its wavelength. If a photographic plate that is only sensitive to bi-photons is positioned behind the double slit, an interference pattern associated with the wavelength L/2 would be observed.
4) States of the form (|20,02), with corresponding L/2 resolution of the interference pattern, have been demonstrated using photons produced by the optical process of "parametric down-conversion"(4,5). In this case, a photon from a pump laser is converted into two photons, each with half the energy of the initial photon.
References (abridged):
1. Dirac, P. A. M. The Principles of Quantum Mechanics (Clarendon, Oxford, 1982)
2. Mitchell, M. W., Lundeen, J. S. & Steinberg, A. M. Nature 429, 161-164 (2004)
3. Walther, P. et al. Nature 429, 158-161 (2004)
4. Ou, Z. Y., Zou, X. Y., Wang, L. J. & Mandel, L. Phys. Rev. A 42, 2957-2965 (1990)
5. Rarity, J. G. Phys. Rev. Lett. 65, 1348-1351 (1990)
Nature http://www.nature.com/nature
--------------------------------
Related Material:
QUANTUM PHYSICS: ON ATOM-PHOTON ENTANGLEMENT
The following points are made by B.B. Blinov (Nature 2004 428:153):
1) An outstanding goal in quantum information science is the faithful mapping of quantum information between a stable quantum memory and a reliable quantum communication channel(1). This would allow, for example, quantum communication over remote distances(2), quantum teleportation(3) of matter, and distributed quantum computing over a "quantum internet".
2) Because quantum states cannot in general be copied, quantum information can only be distributed in these and other applications by entangling the quantum memory with the communication channel.
3) Atom-photon entanglement has been implicit in many previous experimental systems, from early measurements of Bell inequality violations in atomic cascade systems to fluorescence studies in trapped atomic ions. A prime example of current interest is strongly coupled cavity quantum electrodynamics, where individual atoms interact with photons in single-mode cavities(5). Another example is the continuous-variable entanglement between ensembles of atoms and light fields observed in systems containing macroscopic numbers of atoms and photons. However, atom-photon entanglement has not been directly observed in previous experiments, as the individual atoms and photons have not been under sufficient control.
4) The authors report quantum entanglement between an ideal quantum memory -- represented by a single trapped 111-Cd+ ion --and an ideal quantum communication channel provided by a single photon emitted spontaneously from the ion. Appropriate coincidence measurements between the quantum states of the photon polarization and the trapped ion memory are used to verify their entanglement directly. The direct observation of entanglement between stationary and "flying" qubits(4) is accomplished without using cavity quantum electrodynamic techniques(5) or prepared non-classical light sources(3). The authors suggest this source of entanglement may be used for a variety of quantum communication protocols(2), and for seeding large-scale entangled states of trapped ion qubits for scalable quantum computing.
References (abridged):
1. DiVincenzo, D. The physical implementation of quantum computation. Fortschr. Phys. 48, 771-783 (2000)
2. Duan, L.-M., Lukin, M., Cirac, J. I. & Zoller, P. Long-distance quantum communication with atomic ensembles and linear optics. Nature 414, 413-418 (2001)
3. Bouwmeester, D., Ekert, A. & Zeilinger, A. (eds) Quantum Cryptography, Quantum Teleportation, Quantum Computation (Springer, Springer, 2000)
4. Gheri, K., Ellinger, K., Pellizzari, T. & Zoller, P. Photon-wavepackets as flying quantum bits. Fortschr. Phys. 46, 401-415 (1998)
5. Haroche, S., Raimond, J. M. & Brune, M. in Experimental Quantum Computation and Information (eds de Martini, F. & Brune, M.) 3-36 (Proc. Int. School of Physics Enrico Fermi, course CXLVIII, IOS Press, Amsterdam, 2002)
Nature http://www.nature.com/nature
--------------------------------
ON QUANTUM ENTANGLEMENT
The following points are made by B.M. Terhal et al (Physics Today 2003 April):
1) Erwin Schroedinger (1887-1961) coined the word entanglement in 1935 in a three-part paper (Naturwiss. 1935 48:807; 49:823,844; Engl. trans.: Proc. Am. Philos. Soc. 1980 124:323) on the "present situation in quantum mechanics." His article was prompted by Albert Einstein, Boris Podolsky, and Nathan Rosen's now celebrated "EPR paper" that had raised fundamental questions about quantum mechanics earlier that year.
2) Einstein and his coauthors had recognized that quantum theory allows very particular correlations to exist between two physically distant parts of a quantum system; those correlations make it possible to predict the result of a measurement on one part of a system by looking at the distant part. On that basis, the EPR paper argued that the distant predicted quantity should have a definite value even before being measured if the theory were to claim completeness and respect locality. However, because quantum mechanics disallows such definite values prior to measuring, the EPR authors concluded that, from a classical perspective, quantum theory must be incomplete.
3) Schroedinger's 1935 perspective comes closer to the modern view: The wavefunction or state vector gives us all the information that we can have about a quantum system. About entangled quantum states, he wrote, "The whole is in a definite state, the parts taken individually are not," which we now understand as the essence of pure-state entanglement. In that same 1935 article, Schroedinger also introduced his famous cat as an extreme illustration of entanglement: A cat physically isolated in a box with a decaying atom and vial of cyanide represents a quantum state having macroscopic degrees of freedom. If the atom were to decay and trigger the release of cyanide, the cat would die. The quantum-mechanical description of the system is a coherent superposition of one state in which the atom is still excited and the cat alive, and another state in which the atom has decayed and the cat is dead. The isolated cat-trigger-atom-cyanide system as a whole is in a definite entangled state, even though the cat itself exists as a probabilistic mixture of being alive or dead.
4) For the three decades following the 1935 articles, the debate about entanglement and the "EPR dilemma" -- how to make sense of the presumably nonlocal effect one particle's measurement has on another -- was philosophical in nature, and for many physicists it was nothing more than that. The 1964 publication (J.S. Bell: Physics 1964 1:195) by John Bell changed that situation dramatically. Bell derived correlation inequalities that can be violated in quantum mechanics but have to be satisfied within every model that is local and complete -- so-called local hidden-variable models. Bell's work made it possible to test whether local hidden-variable models can account for observed physical phenomena. Early and ongoing recent experiments showing violations of such Bell inequalities have invalidated local hidden-variable models and lend support to the quantum-mechanical view of nature. In particular, an observed violation of a Bell inequality demonstrates the presence of entanglement in a quantum system.
Physics Today http://www.physicstoday.org
ScienceWeek http://scienceweek.com
|