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Register a new userEinsteins Recoiling Slit Experiment, Complementarity and Uncertainty
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We analyze Einsteins recoiling slit experiment and point out that the inevitable entanglement between the particle and the recoiling-slit was not part of Bohrs reply. We show that if this entanglement is taken into account, one can provided a simpler answer to Einstein. We also derive the Englert-Greenberger-Yasin duality relation from this entanglement. In addition, we show that the Englert-Greenberger-Yasin duality relation can also be thought of as a consequence of the sum uncertainty relation for certain observables of the recoiling slit. Thus, the uncertainty relations and entanglement are both an integral part of the which-way detection process.
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A which-way measurement in Youngs double-slit will destroy the interference pattern. Bohr claimed this complementarity between wave- and particle behaviour is enforced by Heisenbergs uncertainty principle: distinguishing two positions a distance s apart transfers a random momentum q sim hbar/s to the particle. This claim has been subject to debate: Scully et al. asserted that in some situations interference can be destroyed with no momentum transfer, while Storey et al. asserted that Bohrs stance is always valid. We address this issue using the experimental technique of weak measurement. We measure a distribution for q that spreads well beyond [-hbar/s, hbar/s], but nevertheless has a variance consistent with zero. This weakvalued momentum-transfer distribution P_{wv}(q) thus reflects both sides of the debate.
A new scheme for a double-slit experiment in the time domain is presented. Phase-stabilized few-cycle laser pulses open one to two windows (``slits) of attosecond duration for photoionization. Fringes in the angle-resolved energy spectrum of varying visibility depending on the degree of which-way information are observed. A situation in which one and the same electron encounters a single and a double slit at the same time is discussed. The investigation of the fringes makes possible interferometry on the attosecond time scale. The number of visible fringes, for example, indicates that the slits are extended over about 500as.
We establish a rigorous quantitative connection between (i) the interferometric duality relation for which-way information and fringe visibility and (ii) Heisenbergs uncertainty relation for position and modular momentum. We apply our theory to atom interferometry, wherein spontaneously emitted photons provide which way information, and unambiguously resolve the challenge posed by the metamaterial `perfect lens to complementarity and to the Heisenberg-Bohr interpretation of the Heisenberg microscope thought experiment.
Uncertainty relations and complementarity relations are core issues in quantum mechanics and quantum information theory. By use of the generalized Wigner-Yanase-Dyson (GWYD) skew information, we derive several uncertainty and complementarity relations with respect to mutually unbiased measurements (MUMs), and general symmetric informationally complete positive operator valued measurements (SIC-POVMs), respectively. Our results include some existing ones as particular cases. We also exemplify our results by providing a detailed example.
We present a unified view of the Berry phase of a quantum system and its entanglement with surroundings. The former reflects the nonseparability between a system and a classical environment as the latter for a quantum environment, and the concept of geometric time-energy uncertainty can be adopted as a signature of the nonseparability. Based on this viewpoint, we study their relationship in the quantum-classical transition of the environment, with the aid of a spin-half particle (qubit) model exposed to a quantum-classical hybrid field. In the quantum-classical transition, the Berry phase has a similar connection with the time-energy uncertainty as the case with only a classical field, whereas the geometric phase for the mixed state of the qubit exhibits a complementary relationship with the entanglement. Namely, for a fixed time-energy uncertainty, the entanglement is gradually replaced by the mixed geometric phase as the quantum field vanishes. And the mixed geometric phase becomes the Berry phase in the classical limit. The same results can be draw out from a displaced harmonic oscillator model.
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