Urbasi Sinha

Ruling Out Multi-Order Interference in Quantum Mechanics

Quantum Mechanics Born to Be Linear Two pillars of modern physics, quantum mechanics and gravity, have so far resisted attempts to be reconciled into one grand theory. This has prompted suggestions that theories about either or both need to be modified at a fundamental level. Sinha et al. (p. 418; see the Perspective by Franson) looked at the interference pattern resulting from a number of slits, to test the “Born rule” of quantum mechanics. They verified that Born holds true—that the interference pattern is built up by the interference from two paths, and two paths only, with no higher-order paths interfering. The result rules out any nonlinear theories of quantum mechanics; thus, any modification of theory will need to take into account that quantum mechanics is linear. A multiple-slit diffraction experiment shows that interference arises from pairs of paths. Quantum mechanics and gravitation are two pillars of modern physics. Despite their success in describing the physical world around us, they seem to be incompatible theories. There are suggestions that one of these theories must be generalized to achieve unification. For example, Born’s rule—one of the axioms of quantum mechanics—could be violated. Born’s rule predicts that quantum interference, as shown by a double-slit diffraction experiment, occurs from pairs of paths. A generalized version of quantum mechanics might allow multipath (i.e., higher-order) interference, thus leading to a deviation from the theory. We performed a three-slit experiment with photons and bounded the magnitude of three-path interference to less than 10−2 of the expected two-path interference, thus ruling out third- and higher-order interference and providing a bound on the accuracy of Born’s rule. Our experiment is consistent with the postulate both in semiclassical and quantum regimes.

Testing Born's Rule in Quantum Mechanics with a Triple Slit Experiment

In Mod. Phys. Lett. A 9, 3119 (1994), one of us (R.D.S) investigated a formulation of quantum mechanics as a generalized measure theory. Quantum mechanics computes probabilities from the absolute squares of complex amplitudes, and the resulting interference violates the (Kolmogorov) sum rule expressing the additivity of probabilities of mutually exclusive events. However, there is a higher order sum rule that quantum mechanics does obey, involving the probabilities of three mutually exclusive possibilities. We could imagine a yet more general theory by assuming that it violates the next higher sum rule. In this paper, we report results from an ongoing experiment which sets out to test the validity of this second sum rule by measuring the interference patterns produced by three slits and all the possible combinations of those slits being open or closed. We use an attenuated laser light combined with single photon counting to confirm the particle character of the measured light.

Nonclassical Paths in Quantum Interference Experiments

In a double slit interference experiment, the wave function at the screen with both slits open is not exactly equal to the sum of the wave functions with the slits individually open one at a time. The three scenarios represent three different boundary conditions and as such, the superposition principle should not be applicable. However, most well-known text books in quantum mechanics implicitly and/or explicitly use this assumption that is only approximately true. In our present study, we have used the Feynman path integral formalism to quantify contributions from nonclassical paths in quantum interference experiments that provide a measurable deviation from a naive application of the superposition principle. A direct experimental demonstration for the existence of these nonclassical paths is difficult to present. We find that contributions from such paths can be significant and we propose simple three-slit interference experiments to directly confirm their existence.

Aharon-Vaidman quantum game with a Young-type photonic qutrit

The Aharon-Vaidman (AV) game exemplifies the advantage of using simple quantum systems to outperform classical strategies. We present an experimental test of this quantum advantage by using a three-state quantum system (qutrit) encoded in a spatial mode of a single photon passing through a system of three slits. The preparation of a particular state is controlled as the photon propagates through the slits by varying the number of open slits and their respective phases. The measurements are achieved by placing detectors in the specific positions in the near and far-field after the slits. This set of tools allowed us to perform tomographic reconstructions of generalized qutrit states, and implement the quantum version of the AV game with compelling evidence of the quantum advantage.

On the superposition principle in interference experiments

The superposition principle is usually incorrectly applied in interference experiments. This has recently been investigated through numerics based on Finite Difference Time Domain (FDTD) methods as well as the Feynman path integral formalism. In the current work, we have derived an analytic formula for the Sorkin parameter which can be used to determine the deviation from the application of the principle. We have found excellent agreement between the analytic distribution and those that have been earlier estimated by numerical integration as well as resource intensive FDTD simulations. The analytic handle would be useful for comparing theory with future experiments. It is applicable both to physics based on classical wave equations as well as the non-relativistic Schrödinger equation.

Temperature-dependent electron mobility in InAs nanowires

Effective electron mobilities are obtained by transport measurements on InAs nanowire field-effect transistors at temperatures ranging from 10 to 200 K. The mobility increases with temperatures below ∼30-50 K, and then decreases with temperatures above 50 K, consistent with other reports. The magnitude and temperature dependence of the observed mobility can be explained by Coulomb scattering from ionized surface states at typical densities. The behaviour above 50 K is ascribed to the thermally activated increase in the number of scatterers, although nanoscale confinement also plays a role as higher radial subbands are populated, leading to interband scattering and a shift of the carrier distribution closer to the surface. Scattering rate calculations using finite-element simulations of the nanowire transistor confirm that these mechanisms are able to explain the data.

The effect of environmental coupling on tunneling of quasiparticles in Josephson junctions

We study quasiparticle tunneling in Josephson tunnel junctions embedded in an electromagnetic environment. We identify tunneling processes that transfer electrical charge and couple to the environment in a way similar to that of normal electrons, and processes that mix electrons and holes and are thus creating charge superpositions. The latter are sensitive to the phase difference between the superconductors and are thus limited by phase diffusion even at zero temperature. We show that the environmental coupling is suppressed in many environments, thus leading to lower quasiparticle decay rates and better superconductor qubit coherence than previously expected. Our approach is nonperturbative in the environmental coupling strength.

Implementing the Aharon-Vaidman quantum game with a Young type photonic qutrit

The Aharon-Vaidman (AV) game exemplifies the advantage of using simple quantum systems to outperform classical strategies. We present an experimental test of this quantum advantage by using a three-state quantum system (qutrit) encoded in a spatial mode of a single photon passing through a system of three slits. The preparation of a particular state is controlled as the photon propagates through the slits by varying the number of open slits and their respective phases. The measurements are achieved by placing detectors in the specific positions in the near and far-field after the slits. This set of tools allowed us to perform tomographic reconstructions of generalized qutrit states, and implement the quantum version of the AV game with compelling evidence of the quantum advantage.

Improving high-TC dc SQUID performance by means of junction asymmetry

We study noise and noise energy of a high-T

On transmission line resonances in high TC dc SQUIDs

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