arXiv subjects

Nikolaj Thomas Zinner

Publications and source records attributed to Nikolaj Thomas Zinner.

32 records · Page 2Linked to original sources

arXiv2019

Native three-body interaction in superconducting circuits

We show how a superconducting circuit consisting of three identical, non-linear oscillators in series considered in terms of its electrical modes can implement a strong, native three-body interaction among qubits. Because of strong interactions, part of the qubit-subspace is coupled to higher levels. The remaining qubit states can be used to implement a restricted Fredkin gate, which in turn implements a CNOT-gate or a spin transistor. Including non-symmetric contributions from couplings to ground and external control we alter the circuit slightly to compensate, and find average fidelities for our implementation of the above gates above $ 99.5\% $ with operation times on the order of a nanosecond. Additionally we show how to analytically include all orders of the cosine contributions from Josephson junctions to the Hamiltonian of a superconducting circuit.

cond-mat.supr-con↗

arXiv2019

Non-existence theorems and solutions of the Wu-Yang monopole equation

We consider the dynamics of the classical $SU(2)$ Wu-Yang monopole problem and show a set of new directions for its analysis starting from a variational setting. This allows us to give a new interpretation of the monopole charge as a string in a centrifugal potential. The field equations are solved using both standard power series, as well as a new Padé approach. Furthermore, we discuss non-existence, and give a proof that rule out even singular non-trivial smooth finite energy solutions. Due to its non-vanishing chromomagnetic fields, the monopole can be interpreted as a collection of magnetic dipoles. Along the same lines, a non-smooth glue-ball solution is discussed that may serve as a toy model of the proton or a radiation-dominated cosmological expansion. Finally, we discuss generalizations of the Wu-Yang monopole.

hep-th↗

arXiv2019

Hybrid Quantum Error Correction in Qubit Architectures

Noise and errors are inevitable parts of any practical implementation of a quantum computer. As a result, large-scale quantum computation will require ways to detect and correct errors on quantum information. Here, we present such a quantum error correcting scheme for correcting the dominant error sources, phase decoherence and energy relaxation, in qubit architectures, using a hybrid approach combining autonomous correction based on engineered dissipation with traditional measurement-based quantum error correction. Using numerical simulations with realistic device parameters for superconducting circuits, we show that this scheme can achieve a 5- to 10-fold increase in storage-time while using only six qubits for the encoding and two ancillary qubits for the operation of the autonomous part of the scheme, providing a potentially large reduction of qubit overhead compared to typical measurement-based error correction schemes. Furthermore, the scheme relies on standard interactions and qubit driving available in most major quantum computing platforms, making it implementable in a wide range of architectures.

quant-ph↗

arXiv2017

Physical approach to quantum networks with massive particles

This paper treats a quantum network from a physical approach, explicitly finds the physical eigenstates and compares them to the quantum-graph description. The basic building block of a quantum network is an X-shaped potential well made by crossing two quantum wires, and we consider a massive particle in such an X well. The system is analyzed using a variational method based on an expansion into modes with fast convergence and it provides a very clear intuition for the physics of the problem. The particle is found to have a ground state that is exponentially localized to the center of the X well, and the other symmetric solutions are formed so to be orthogonal to the ground state. This is in contrast to the predictions of the conventionally used so-called Kirchoff boundary conditions in quantum graph theory that predict a different sequence of symmetric solutions that cannot be physically realized. Numerical methods have previously been the only source of information on the ground-state wave function and our results provide a different perspective with strong analytical insights. The ground-state wave function has the shape of a solitonic solution to the non-linear Schr{ö}dinger equation, enabling an analytical prediction of the wave number. When combining multiple X wells into a network or grid, each site supports a solitonic localized state. The solitons only couple to each other and are able to jump from one site to another as if they were trapped in a discrete lattice.

cond-mat.mes-hall↗

arXiv2017

The Goldilocks model of separable, zero-range, few-body interactions in one-dimensional harmonic traps

This article introduces the "Goldilocks model" for a few repulsively interacting particles trapped in a one-dimensional harmonic well and provides exact solutions for the three-particle case. The Goldilocks model shares features with two other well-known systems, the Calogero model and the contact-interaction model, and coincides with them in limiting cases. However, those models have purely two-body interactions whereas this model has intrinsically few-body interactions. Comparing these three models provides clarifying distinctions among the properties of symmetry, separability and integrability. The model's analytic solutions provide a useful basis to improve approximation schemes, especially near the unitary limit of hard-core contact interactions.

quant-ph↗

arXiv2016

Quantum collision theory in flat bands

We consider quantum scattering of particles in media exhibiting strong dispersion degeneracy. In particular, we study flat-banded lattices and linearly dispersed energy bands. The former constitute a prime example of single-particle frustration while the latter show degeneracy at the few- and many-particle level. We investigate both impurity and two-body scattering and show that, quite generally, scattering does not occur, which we relate to the fact that transition matrices vanish on the energy shell. We prove that scattering is instead replaced by projections onto band-projected eigenstates of the interaction potential. We then use the general results to obtain localised flat band states that are eigenstates of impurity potentials with vanishing eigenvalues in one-dimensional flat bands and study the particular case of a sawtooth lattice. We also uncover the relation between certain solutions of one-dimensional systems that have been categorised as "strange", and the scattering states in linearly dispersed continuum systems.

cond-mat.quant-gas↗

arXiv2016

Unitary fermions and Luscher's formula on a crystal

We consider the low-energy particle-particle scattering properties in a periodic simple cubic crystal. In particular, we investigate the relation between the two-body scattering length and the energy shift experienced by the lowest-lying unbound state when this is placed in a periodic finite box. We introduce a continuum model for s-wave contact interactions that respects the symmetry of the Brillouin zone in its regularisation and renormalisation procedures, and corresponds to the na{ï}ve continuum limit of the Hubbard model. The energy shifts are found to be identical to those obtained in the usual spherically symmetric renormalisation scheme upon resolving an important subtlety regarding the cutoff procedure. We then particularize to the Hubbard model, and find that for large finite lattices the results are identical to those obtained in the continuum limit. The results reported here are valid in the weak, intermediate and unitary limits, and can be used for the extraction of scattering information ,via exact diagonalisation or Monte Carlo methods, of two-body systems in realistic periodic lattices.

cond-mat.quant-gas↗

arXiv2016

Exploring the few- to many-body crossover using cold atoms in one dimension

Cold atomic gases have provided us with a great number of opportunities for studying various physical systems under controlled conditions that are seldom offered in other fields. We are thus at the point where one can truly do quantum simulation of models that are relevant for instance in condensed-matter or high-energy physics, i.e. we are on the verge of a 'cool' quantum simulator as envisioned by Feynman. One of the avenues under exploration is the physics of one-dimensional systems. Until recently this was mostly in the many-body limit but now experiments can be performed with controllable particle numbers all the way down to the few-body regime. After a brief introduction to some of the relevant experiments, I will review recent theoretical work on one-dimensional quantum systems containing bosons, fermions, or mixtures of the two, with a particular emphasis on the case where the particles are held by an external trap.

quant-ph↗

arXiv2014

Efimov three-body states on top of a Fermi sea

The stabilization of Cooper pairs of bound electrons in the background of a Fermi sea is the origin of superconductivity and the paradigmatic example of the striking influence of many-body physics on few-body properties. In the quantum-mechanical three-body problem the famous Efimov effect yields unexpected scaling relations among a tower of universal states. These seemingly unrelated problems can now be studied in the same setup thanks to the success of ultracold atomic gas experiments. In light of the tremendous effect of a background Fermi sea on two-body properties, a natural question is whether a background can modify or even destroy the Efimov effect. Here we demonstrate how the generic problem of three interacting particles changes when one particle is embedded in a background Fermi sea, and show that Efimov scaling persists. It is found in a scaling that relates the three-body physics to the background density of fermionic particles.

cond-mat.quant-gas↗

arXiv2014

Dipoles on a Two-leg Ladder

We study polar molecules with long-range dipole-dipole interactions confined to move on a two-leg ladder for different orientations of the molecular dipole moments with respect to the ladder. Matrix product states are employed to calculate the many-body ground state of the system as function of lattice filling fractions, perpendicular hopping between the legs, and dipole interaction strength. We show that the system exhibits zig-zag ordering when the dipolar interactions are predominantly repulsive. As a function of dipole moment orientation with respect to the ladder, we find that there is a critical angle at which ordering disappears. This angle is slightly larger than the angle at which the dipoles are non-interacting along a single leg. This behavior should be observable using current experimental techniques.

cond-mat.quant-gas↗

arXiv2012

Vortex Structures in a Rotating BEC Dark Matter Component

We study the effects of a dark matter component that consists of bosonic particles with ultralight masses in the condensed state. We compare previous studies for both non-interacting condensates and with repulsive two-body terms and show consistency between the proposals. Furthermore, we explore the effects of rotation on a superfluid dark matter condensate, assuming that a vortex lattice forms as seen in ultracold atomic gas experiments. The influence of such a lattice in virialization of gravitationally bound structures and on galactic rotation velocity curves is explored. With fine-tuning of the bosonic particle mass and the two-body repulsive interaction strength, we find that one can have sub-structure on rotation curves that resembles some observations in spiral galaxies. This occurs when the dark matter halo has an array of hollow cylinders. This can cause oscillatory behavior in the galactic rotation curves in similar fashion to the well-known effect of the spiral arms. We also consider how future experiments and numerical simulations with ultracold atomic gases could tell us more about such exotic dark matter proposals.

astro-ph.CO↗

arXiv2011

Galactic abundances as a relic neutrino detection scheme

We propose to use the threshold-free process of neutrino capture on beta-decaying nuclei (NCB) using all available candidate nuclei in the Milky Way as target material in order to detect the presence of the Cosmic neutrino background. By integrating over the lifetime of the galaxy one might be able to see the effect of NCB processes as a slightly eschewed abundance ratio of selected beta-decaying nuclei. First, the candidates must be chosen so that both the mother and daughter nuclei have a lifetime comparable to that of the Milky Way or the signal could be easily washed out by additional decays. Secondly, relic neutrinos have so low energy that their de Broglie wavelengths are macroscopic and they may therefore scatter coherently on the electronic cloud of the candidate atoms. One must therefore compare the cross sections for the two processes (induced beta-decay by neutrino capture, and coherent scattering of the neutrinos on atomic nuclei) before drawing any conclusions. Finally, the density of target nuclei in the galaxy must be calculated. We assume supernovae as the only production source and approximate the neutrino density as a homogenous background. Here we perform the full calculation for 187-Re and 138-La and find that one needs abundance measurements with 24 digit precision in order to detect the effect of relic neutrinos. Or alternatively an enhancement of of the relic neutrino density by a factor of $10^{15}$ to produce an effect within the current abundance measurement precision.

astro-ph.CO↗

arXiv2006

Alpha decay rate enhancement in metals: An unlikely scenario

It has been recently suggested that one might drastically shorten the alpha lifetime of nuclear waste products, if these are embedded in metals at low temperatures. Using quantum mechanical tunneling arguments, we show that such an effect is likely to be very small, if present at all.

nucl-th↗

arXiv2006

Muon capture on nuclei: random phase approximation evaluation versus data for 6 $\le$ Z $\le$ 94 nuclei

We use the random phase approximation to systematically describe the total muon capture rates on all nuclei where they have been measured. We reproduce the experimental values on these nuclei to better than 15% accuracy using the free nucleon weak form factors and residual interactions with a mild $A$ dependency. The isospin dependence and the effects associated with shell closures are fairly well reproduced as well. However, the calculated rates for the same residual interactions would be significantly lower than the data if the in-medium quenching of the axial-vector coupling constant is employed to other than the true Gamow-Teller amplitudes. Our calculation thus suggests that no quenching is needed in the description of semileptonic weak processes involving higher multipole transitions and momentum transfer $\sim m_μ$, with obvious importance to analogous weak processes.

nucl-th↗