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Register a new userFringe visibility and distinguishability in two-path interferometer with an asymmetric beam splitter
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We study the fringe visibility and the distinguishability of a general Mach-Zehnder interferometer with an asymmetric beam splitter. Both the fringe visibility V and the distinguishability D are affected by the input state of the particle characterized by the Bloch vector S=(Sx,Sy,Sz) and the second asymmetric beam splitter characterized by paramter /beta. For the total system is initially in a pure state, it is found that the fringe visibility reaches the upper bound and the distinguishability reaches the lower bound when cos(/beta) = -Sx. The fringe visibility obtain the maximum only if Sx = 0 and /beta = /pi/2 when the input particle is initially in a mixed state. The complementary relationship V2 + D2 <= 1 is proved in a general Mach-Zehnder interferometer with an asymmetric beam splitter, and the conditions for the equality are also presented.
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By using an asymmetric beam splitter, we observe the generalized Hong-Ou-Mandel effects for three and four photons, respectively. Furthermore, we can use this generalized Hong-Ou-Mandel interferometer to characterize temporal distinguishability.
We have constructed an asymmetric matter-wave beam splitter and a ring potential on an atom chip with Bose-Einstein condensates using radio-frequency dressing. By applying rf-field parallel to the quantization axis in the vicinity of the static trap minima added to perpendicular rf-fields, versatile controllability on the potentials is realized. Asymmetry of the rf-induced double well is manipulated without discernible displacement of the each well along horizontal and vertical direction. Formation of an isotropic ring potential on an atom chip is achieved by compensating the gradient due to gravity and inhomogeneous coupling strength. In addition, position and rotation velocity of a BEC along the ring geometry are controlled by the relative phase and the frequency difference between the rf-fields, respectively.
We construct a matter-wave beam splitter using 87Rb Bose-Einstein condensate on an atom chip. Through the use of radio-frequency-induced double-well potentials, we were able to split a BEC into two clouds separated by distances ranging from 2.8 {mu}m to 57 {mu}m. Interference between these two freely expanding BECs has been observed. By varying the rf-field amplitude, frequency, or polarization, we investigate behaviors of the beam-splitter. From the perspective of practical use, our BEC manipulation system is suitable for application to interferometry since it is compact and the repetition rate is high due to the anodic bonded atom chip on the vacuum cell. The portable system occupies a volume of 0.5 m3 and operates at a repetition rate as high as ~0.2 Hz.
This paper systematically develops the resource theory of asymmetric distinguishability, as initiated roughly a decade ago [K. Matsumoto, arXiv:1010.1030 (2010)]. The key constituents of this resource theory are quantum boxes, consisting of a pair of quantum states, which can be manipulated for free by means of an arbitrary quantum channel. We introduce bits of asymmetric distinguishability as the basic currency in this resource theory, and we prove that it is a reversible resource theory in the asymptotic limit, with the quantum relative entropy being the fundamental rate of resource interconversion. The distillable distinguishability is the optimal rate at which a quantum box consisting of independent and identically distributed (i.i.d.) states can be converted to bits of asymmetric distinguishability, and the distinguishability cost is the optimal rate for the reverse transformation. Both of these quantities are equal to the quantum relative entropy. The exact one-shot distillable distinguishability is equal to the min-relative entropy, and the exact one-shot distinguishability cost is equal to the max-relative entropy. Generalizing these results, the approximate one-shot distillable distinguishability is equal to the smooth min-relative entropy, and the approximate one-shot distinguishability cost is equal to the smooth max-relative entropy. As a notable application of the former results, we prove that the optimal rate of asymptotic conversion from a pair of i.i.d. quantum states to another pair of i.i.d. quantum states is fully characterized by the ratio of their quantum relative entropies.
We study both the wave-like behavior and particle-like behavior in a general Mach-Zehnder interferometer with its asymmetric beam splitter. A error-free measurement in the detector is used to extract the which-path information. The fringe visibility V and the which-path information Ipath are derived: their complementary relation V + Ipath less than or equal to 1 are found, and the condition for the equality is also presented.
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