Heisenberg in 1929 introduced the “collapse of the wavepacket” into quantum theory. We review here an experiment at Berkeley which demonstrated several aspects of this idea. In this experiment, a pair of daughter photons was produced in an entangled state, in which the sum of their two energies was equal to the sharp energy of their parent photon, in the nonlinear optical process of spontaneous parametric down-conversion. The wavepacket of one daughter photon collapsed upon a measurement-at-a-distance of the other daughter's energy, in such a way that the total energy of the two-photon system was conserved. Heisenberg's energy-time uncertainty principle was also demonstrated to hold in this experiment.
Heisenberg in 1929 introduced the “collapse of the wavepacket” into quantum theory. We review here an experiment at Berkeley which demonstrated several aspects of this idea. In this experiment, a pair of daughter photons was produced in an entangled state, in which the sum of their two energies was equal to the sharp energy of their parent photon, in the nonlinear optical process of spontaneous parametric down-conversion. The wavepacket of one daughter photon collapsed upon a measurement-at-a-distance of the other daughter's energy, in such a way that the total energy of the two-photon system was conserved. Heisenberg's energy-time uncertainty principle was also demonstrated to hold in this experiment.
The energy-time uncertainty principle is on a different footing than the momentum position uncertainty principle: in contrast to position, time is a c-number parameter, and not an operator. As Aharonov and Bohm have pointed out, this leads to different interpretations of the two uncertainty principles. In particular, one must distinguish between an inner and an outer time in the definition of the spread in time, delta t. It is the inner time which enters the energy-time uncertainty principle. We have checked this by means of a correlated two-photon light source in which the individual energies of the two photons are broad in spectra, but in which their sum is sharp. In other words, the pair of photons is in an entangled state of energy. By passing one member of the photon pair through a filter with width delta E, it is observed that the other member's wave packet collapses upon coincidence detection to a duration delta t, such that delta E(delta t) is approximately equal to planks constant/2 pi, where this duration delta t is an inner time, in the sense of Aharonov and Bohm. We have measured delta t by means of a Michelson interferometer by monitoring the visibility of the fringes seen in coincidence detection. This is a nonlocal effect, in the sense that the two photons are far away from each other when the collapse occurs. We have excluded classical-wave explanations of this effect by means of triple coincidence measurements in conjunction with a beam splitter which follows the Michelson interferometer. Since Bell's inequalities are known to be violated, we believe that it is also incorrect to interpret this experimental outcome as if energy were a local hidden variable, i.e., as if each photon, viewed as a particle, possessed some definite but unknown energy before its detection.
Two photons in a pair generated in the nonlinear optical process of spontaneous parametric down-conversion are, in general, strongly quantum entangled. Accordingly, they contain extremely strong energy, time, polarization and momentum quantum correlations. This entanglement involves more than one quantum variable and has served as a powerful tool in fundamental studies of quantum theory. It is now playing a large role in the development of novel information processing techniques and new optical measurement technologies. Here we review some of these technologies and their origins.
The Physics Teacher ◆ Vol. 50, May 2012 DOI: 10.1119/1.3703540 are really two parts of a single black-and-green packet. Even if widely separated in space, they form a single unified field quantum. This is similar to a one-particle wave packet that is separated into two parts (e.g., a photon that has interacted with a half-reflecting mirror and is now a superposition of a wave packet that passed through the mirror and a packet that reflected from the mirror), but now there is a real excitation in each of the two parts. In classes for scientists or engineers, you could follow this qualitative description with an algebraic description.5 One popular entanglement method, used in the experiment described below, is called “spontaneous parametric down-conversion.” When photons pass through a certain kind of nonlinear crystal, a tiny fraction of them split into two photons of equal energy. It’s not understood why this occurs, but Leonard Mandel of the University of Rochester discovered that each pair of daughter photons is entangled. If one of the two entangled particles experiences a macroscopic interaction, for example by striking a viewing screen, that portion of the two-particle wave packet instantly collapses everywhere. According to quantum physics, this instantly affects the other particle, even if the two are light-years apart. Anton Zeilinger’s group has confirmed this effect at distances up to 144 kilometers.6 Alain Aspect’s group has confirmed that the second particle alters its state in response to an interaction of the first particle in a time shorter than is required for light to connect the two particles.7 It’s an irony of physics Teaching Quantum Nonlocality1
Based on the quantum behavior of entangled photon pairs generated via spontaneous parametric down conversion, this paper reviews the concept of effective two-photon wavefunction or biphoton wavepacket and emphasize the very different physics associated with the entangled two-photon system and with its "individual" subsystems. Experimental approaches for Bell state preparation, pumped by continuous wave and ultrashort pulse, and the propagation of biphoton wavepacket in dispersive media are discussed.
One of the most surprising consequences of quantum mechanics is the entanglement of two or more distance particles. Even though there are still questions regarding the fundamental issues of quantum theory, quantum entanglement has started to play important roles in practical engineering applications such as quantum information processing, quantum metrology, quantum imaging and quantum lithography. Two-photon states have been the most popular entangled states in fundamental and applied research. Using spontaneous parametric down conversion as an example, this review introduces the concept of biphoton wavepacket and emphasizes the very different physics associated with the entangled two-photon system (pure state) and with the `individual' subsystems (statistical mixture). Experimental approaches for Bell state preparation, pumped by continous wave and ultrashort pulse are discussed.
Summary form only given. In early 1930's, Karl Popper, a metaphysical realist, proposed a thought experiment to support his realistic interpretation of quantum mechanics, which shared the same goal of the EPR gedankenexperiment. Based on the same EPR two-particle entangled state, Popper asked: if the precise position of particle 2 is known due to the precise measurement of the position for its entangled twin particle 1, does particle 2 experience a greater uncertainty in its momentum? This question has been ignored for many years. One may not like Popper's philosophy of quantum mechanics; however, his question is closely related to an important problem in recent hot applications: what one can predict for the remaining parts of an entangled state if one of the subsystems is measured alone? We have realized Popper's experiment with the use of entangled two-photon source of spontaneous parametric down conversion. We conclude from this experiment: in an entangled two-particle system, the precise knowledge of the position of a particle, which is determined by the two-particle entanglement, does not necessarily produce an uncertainty in its momentum.