Analysis of the SN1987A two-stage explosion hypothesis with account for the MSW neutrino flavour conversion

Detection of 5 events by the Liquid Scintillation Detector (LSD) on February, 23, 1987 was interpreted in the literature as the detection of neutrinos from the first stage of the two-stage supernova collapse. We pose rigid constraints on the properties of the first stage of the collapse, taking into account neutrino flavour conversion due to the MSW-effect and general properties of supernova neutrino emission. The constraints depend on the unknown neutrino mass hierarchy and mixing angle \theta_{13}.Comment: presented at "Rencontres de Moriond EW 2007", 10-17 March 200

Perpetual motion of a mobile impurity in a one-dimensional quantum gas

Consider an impurity particle injected in a degenerate one-dimensional gas of noninteracting fermions (or, equivalently, Tonks-Girardeau bosons) with some initial momentum $p_0$. We examine the infinite-time value of the momentum of the impurity, $p_\infty$, as a function of $p_0$. A lower bound on $|p_\infty(p_0)|$ is derived under fairly general conditions. The derivation, based on the existence of the lower edge of the spectrum of the host gas, does not resort to any approximations. The existence of such bound implies the perpetual motion of an impurity in a one-dimensional gas of noninteracting fermions or Tonks-Girardeau bosons at zero temperature. The bound has an especially simple and useful form when the interaction between the impurity and host particles is everywhere repulsive

A necessary condition for quantum adiabaticity applied to the adiabatic Grover search

Numerous sufficient conditions for adiabaticity of the evolution of a driven quantum system have been known for quite a long time. In contrast, necessary adiabatic conditions are scarce. A practicable necessary condition well-suited for many-body systems has been proven recently in [Phys. Rev. Lett. 119, 200401 (2017)]. Here we tailor this condition for estimating run times of quantum adiabatic algorithms. As an illustration, the condition is applied to the adiabatic algorithm for searching in an unstructured database (adiabatic Grover search algorithm). We find that thus obtained lower bound on the run time of this algorithm reproduces $\sqrt N$ scaling ($N$ being the number of database entries) of the explicitly known optimal run time. This observation highlights the merits of the new adiabatic condition and its potential relevance to adiabatic quantum computing

Constraints on neutrino mixing angle theta_13 and Supernova neutrino fluxes from the LSD neutrino signal from SN1987A

Detection of 5 events by the Liquid Scintillation Detector (LSD) on February, 23, 1987 was recently interpreted as a detection of the electron neutrino flux from the first stage of the two-stage Supernova collapse. We show that, if neutrino mass hierarchy is normal, such interpretation excludes values of neutrino mixing angle \theta_{13} larger than 3\cdot 10^{-2}, independently of the particular Supernova collapse model. Also constraints on the original fluxes of neutrinos and antineutrinos of different flavours are obtained.Comment: 6 pages, no figure

A remark on the notion of independence of quantum integrals of motion in the thermodynamic limit

Studies of integrable quantum many-body systems have a long history with an impressive record of success. However, surprisingly enough, an unambiguous definition of quantum integrability remains a matter of an ongoing debate. We contribute to this debate by dwelling upon an important aspect of quantum integrability -- the notion of independence of quantum integrals of motion (QIMs). We point out that a widely accepted definition of functional independence of QIMs is flawed, and suggest a new definition. Our study is motivated by the PXP model -- a model of $N$ spins $1/2$ possessing an extensive number of binary QIMs. The number of QIMs which are independent according to the common definition turns out to be equal to the number of spins, $N$. A common wisdom would then suggest that the system is completely integrable, which is not the case. We discuss the origin of this conundrum and demonstrate how it is resolved when a new definition of independence of QIMs is employed

Neutrino magnetic moment signatures in the supernova neutrino signal

It is known that if neutrino is a Dirac fermion with magnetic moment, then \nu_L -> \nu_R -> \nu_L transition of supernova neutrinos may occur. The first stage of such transition is due to the neutrino spin flip inside the hot dense supernova core, while the second one - due to the neutrino spin precession in the galactic magnetic field on the way from the supernova to terrestrial detectors. This can result in the detection of 60-200 MeV neutrinos simultaneously with the "normal" supernova neutrino signal, which would be a smoking gun for the Dirac neutrino magnetic moment, \mu. We argue that in case of a nearby supernova explosion (~10 kpc away from the Earth) one may observe such high-energy events in Super-Kamiokande if \mu \gtrsim 10^{-13} \mu_B, and in a Mt-scale detector if \mu \gtrsim 0.5*10^{-13} \mu_B. Such an observation by itself, however, may be not sufficient to determine the value of the magnetic moment, because of the ignorance of the interstellar magnetic field. We point out that if in addition a deficit of the neutronization burst neutrinos is established, it would be possible to extract the value of the magnetic moment from observations. We also briefly discuss a possible Majorana magnetic moment signature due to \nu_e -> \bar{\nu}_{\mu,\tau} flip inside the supernova core

Large quantum superpositions of a nanoparticle immersed in superfluid helium

Preparing and detecting spatially extended quantum superpositions of a massive object comprises an important fundamental test of quantum theory. These quantum states are extremely fragile and tend to quickly decay into incoherent mixtures due to the environmental decoherence. Experimental setups considered up to date address this threat in a conceptually straightforward way -- by eliminating the environment, i.e. by isolating an object in a sufficiently high vacuum. We show that another option exists: decoherence is suppressed in the presence of a strongly interacting environment if this environment is superfluid. Indeed, as long as an object immersed in a pure superfluid at zero temperature moves with a velocity below the critical one, it does not create, absorb or scatter any excitations of the superfluid. Hence, in this idealized situations the decoherence is absent. In reality the decoherence will be present due to thermal excitations of the superfluid and impurities contaminating the superfluid. We examine various decoherence channels in the superfluid $^4$He. It is shown that the total decoherence time can be as large as tens of seconds for a $10^6$ amu nanoparticle delocalized over $300$ nm in helium at $1$ mK. Performing interference experiments in superfluid helium can provide certain practical advantages compared to conventional schemes, e.g. compensation of gravity by the buoyancy force and effective cooling

Perpetual motion and driven dynamics of a mobile impurity in a quantum fluid

We study the dynamics of a mobile impurity in a quantum fluid at zero temperature. Two related settings are considered. In the first setting the impurity is injected in the fluid with some initial velocity ${\mathbf v}_0$, and we are interested in its velocity at infinite time, ${\mathbf v}_\infty$. We derive a rigorous upper bound on $|{\mathbf v}_0-{\mathbf v}_\infty|$ for initial velocities smaller than the generalized critical velocity. In the limit of vanishing impurity-fluid coupling this bound amounts to ${\mathbf v}_\infty={\mathbf v}_0$ which can be regarded as a rigorous proof of the Landau criterion of superfluidity. In the case of a finite coupling the velocity of the impurity can drop, but not to zero; the bound quantifies the maximal possible drop. In the second setting a small constant force is exerted upon the impurity. We argue that two distinct dynamical regimes exist -- backscattering oscillations of the impurity velocity and saturation of the velocity without oscillations. For fluids with $v_{c {\rm L}}=v_s$ (where $v_{c {\rm L}}$ and $v_s$ are the Landau critical velocity and sound velocity, respectively) the latter regime is realized. For fluids with $v_{c {\rm L}} < v_s$ both regimes are possible. Which regime is realized in this case depends on the mass of the impurity, a nonequilibrium quantum phase transition occurring at some critical mass. Our results are equally valid in one, two and three dimensions.Comment: v4: published versio

Decoherence at the level of eigenstates

An eigenstate decoherence hypothesis states that each individual eigenstate of a large closed system is locally classical-like. We extend this hypothesis to account for a typically extremely short time scale of decoherence. The extension implies that nondiagonal matrix elements of certain operators - quantumness witnesses - are suppressed as long as the energy difference between corresponding eigenstates is smaller than the inverse decoherence time

Entangling problem Hamiltonian for adiabatic quantum computation

Adiabatic quantum computation starts from embedding a computational problem into a Hamiltonian whose ground state encodes the solution to the problem. This problem Hamiltonian, $H_{\rm p}$, is normally chosen to be diagonal in the computational basis, that is a product basis for qubits. We point out that $H_{\rm p}$ can be chosen to be non-diagonal in the computational basis. To be more precise, we show how to construct $H_{\rm p}$ in such a way that all its excited states are entangled with respect to the qubit tensor product structure, while the ground state is still of the product form and encodes the solution to the problem. We discuss how such entangling problem Hamiltonians can improve the performance of the adiabatic quantum computation.Comment: v2: entanglement entropy of excited states addressed numericall