Quantum Zero-point Motion Research Articles

Direct observation of a magnetic-field-induced Wigner crystal.

Wigner predicted that when the Coulomb interactions between electrons become much stronger than their kinetic energy, electrons crystallize into a closely packed lattice1. A variety of two-dimensional systems have shown evidence for Wigner crystals2-11 (WCs). However, a spontaneously formed classical or quantum WC has never been directly visualized. Neither the identification of the WC symmetry nor direct investigation of its melting has been accomplished. Here we use high-resolution scanning tunnelling microscopy measurements to directly image a magnetic-field-induced electron WC in Bernal-stacked bilayer graphene and examine its structural properties as a function of electron density, magnetic field and temperature. At high fields and the lowest temperature, we observe a triangular lattice electron WC in the lowest Landau level. The WC possesses the expected lattice constant and is robust between filling factor ν ≈ 0.13 and ν ≈ 0.38 except near fillings where it competes with fractional quantum Hall states. Increasing the density or temperature results in the melting of the WC into a liquid phase that is isotropic but has a modulated structure characterized by the Bragg wavevector of the WC. At low magnetic fields, the WC unexpectedly transitions into an anisotropic stripe phase, which has been commonly anticipated to form in higher Landau levels. Analysis of individual lattice sites shows signatures that may be related to the quantum zero-point motion of electrons in the WC lattice.

Many-body quantum muon effects and quadrupolar coupling in solids

Strong quantum zero-point motion (ZPM) of light nuclei and other particles is a crucial aspect of many state-of-the-art quantum materials. However, it has only recently begun to be explored from an ab initio perspective, through several competing approximations. Here we develop a unified description of muon and light nucleus ZPM and establish the regimes of anharmonicity and positional quantum entanglement where different approximation schemes apply. Via density functional theory and path-integral molecular dynamics simulations we demonstrate that in solid nitrogen, α–N2, muon ZPM is both strongly anharmonic and many-body in character, with the muon forming an extended electric-dipole polaron around a central, quantum-entangled [N2–μ–N2]+ complex. By combining this quantitative description of quantum muon ZPM with precision muon quadrupolar level-crossing resonance experiments, we independently determine the static 14N nuclear quadrupolar coupling constant of pristine α–N2 to be –5.36(2) MHz, a significant improvement in accuracy over the previously-accepted value of –5.39(5) MHz, and a validation of our unified description of light-particle ZPM.

The electron-phonon renormalization in the electronic structure calculation: Fundamentals, current status, and challenges.

Electron-phonon (e-ph) interaction plays a crucial role in determining many physical properties of the materials, such as the superconducting transition temperature, the relaxation time and mean free path of hot carriers, the temperature dependence of the electronic structure, and the formation of the vibrational polaritons. In the past two decades, the calculations of e-ph properties from first-principles has become possible. In particular, the renormalization of electronic structures due to e-ph interaction can be evaluated, providing greater insight into the quantum zero-point motion effect and the temperature dependence behavior. In this perspective, we briefly overview the basic theory, outline the computational challenges, and describe the recent progress in this field, as well as future directions and opportunities of the e-ph coupling calculations.

Spin current Kondo effect in frustrated Kondo systems

Magnetic frustrations can enhance quantum zero-point motion in spin systems and lead to exotic topological insulating states. When coupled to mobile electrons, they may lead to unusual non-Fermi liquid or metallic spin liquid states whose nature has not been well explored. Here, we propose a spin current Kondo mechanism underlying a series of non-Fermi liquid phases on the border of Kondo and magnetic phases in a frustrated three-impurity Kondo model. This mechanism is confirmed by renormalization group analysis and describes movable Kondo singlets called "holons" induced by an effective coupling between the spin current of conduction electrons and the vector chirality of localized spins. Similar mechanism may widely exist in all frustrated Kondo systems and be detected through spin-current noise measurements.

Large Quantum Delocalization of a Levitated Nanoparticle Using Optimal Control: Applications for Force Sensing and Entangling via Weak Forces.

We propose to optimally control the harmonic potential of a levitated nanoparticle to quantum delocalize its center-of-mass motional state to a length scale orders of magnitude larger than the quantum zero-point motion. Using a bang-bang control of the harmonic potential, including the possibility of inverting it, the initial ground-state-cooled levitated nanoparticle coherently expands to large scales and then contracts to the initial state in a time-optimal way. We show that this fast loop protocol can be used to enhance force sensing as well as to dramatically boost the entangling rate of two weakly interacting nanoparticles. We parameterize the performance of the protocol, and therefore the macroscopic quantum regime that could be explored, as a function of displacement and frequency noise in the nanoparticle's center-of-mass motion. This noise analysis accounts for the sources of decoherence relevant to current experiments.

Evidence of zero-point fluctuation of vortices in a very weakly pinned a -MoGe thin film

In a Type II superconductor, the vortex core behaves like a normal metal. Consequently, the single-particle density of states in the vortex core of a conventional Type II superconductor remains either flat or (for very clean single crystals) exhibits a peak at zero bias due to the formation of Caroli-de Gennes-Matricon bound state inside the core. Here we report an unusual observation from scanning tunneling spectroscopy measurements in a weakly pinned thin film of the conventional s-wave superconductor a-MoGe, namely, that a soft gap in the local density of states continues to exist even at the center of the vortex core. We ascribe this observation to rapid fluctuation of vortices about their mean position that blurs the boundary between the gapless normal core and the gapped superconducting region outside. Analyzing the data as a function of magnetic field we show that the variation of fluctuation amplitude as a function of magnetic field is consistent with quantum zero-point motion of vortices.

Violent relaxation in quantum fluids with long-range interactions.

Violent relaxation is a process that occurs in systems with long-range interactions. It has the peculiar feature of dramatically amplifying small perturbations, and rather than driving the system to equilibrium, it instead leads to slowly evolving configurations known as quasistationary states that fall outside the standard paradigm of statistical mechanics. Violent relaxation was originally identified in gravity-driven stellar dynamics; here, we extend the theory into the quantum regime by developing a quantum version of the Hamiltonian mean field (HMF) model which exemplifies many of the generic properties of long-range interacting systems. The HMF model can either be viewed as describing particles interacting via a cosine potential, or equivalently as the kinetic XY model with infinite-range interactions, and its quantum fluid dynamics can be obtained from a generalized Gross-Pitaevskii equation. We show that singular caustics that form during violent relaxation are regulated by interference effects in a universal way described by Thom's catastrophe theory applied to waves and this leads to emergent length scales and timescales not present in the classical problem. In the deep quantum regime we find that violent relaxation is suppressed altogether by quantum zero-point motion. Our results are relevant to laboratory studies of self-organization in cold atomic gases with long-range interactions.

Magnification of signatures of a topological phase transition by quantum zero point motion

In this letter we show that the zero-point motion of the vortex in superconducting doped topological insulators leads to significant changes in the electronic spectrum at the topological phase transition in this system. This topological phase transition is tuned by the doping level and the corresponding effects manifest in the density of states at energies which are of the order of the fluctuations frequency. This frequency might be much larger than the electronic energy gap in the spectrum generated by a stationary vortex. As a result the quantum zero-point motion can move the spectral signature of the topological vortex phase transition to energies which are well within the resolution of scanning tunneling microscopy. Moreover, the phenomena studied in this letter present novel effects of Magnus force on the vortex spectrum which are not present in the ordinary s-wave superconductors. Our results show that quantum zero point fluctuations can bring the fingerprints of topological phase transitions to more experimentally accessible grounds and point to the importance of study of quantum fluctuations in different candidates for realizing topological phase transitions.

Structural flexibility of DNA-like conformers of canonical 2′-deoxyribonucleosides

Relaxed force constants (RFC) and vibrational root-mean-square (VRMS) deviations are used for comparative characterization of mechanical properties of canonical 2'-deoxyribonucleosides (2DRs) and 1,2-dideoxyribose molecule, their model sugar residue. It has been shown that RFC and VRMS should be preferred over traditional force constants when one needs to obtain the quantitative measure of the 'collective' parameter flexibility (furanose sugar pseudorotation phase P in particular) and compare it with classical torsion angles (β, γ, ε, χ). It has been found that torsions ε and β determining the 2DRs backbone hydroxyl orientations are as soft as the pseudorotation phase P with RFC values within 1-10 kcal mol(-1) rad(-2) depending on conformation. Torsion γ is the most rigid one with RFC 15-30 kcal mol(-1) rad(-2), while the glycosidic torsion χ is characterized by intermediate values of RFC (typically 5-10 kcal mol(-1) rad(-2)) and its RFC changes by 10 times, depending on the furanose sugar conformation (K(χ)≈ 3 kcal mol(-1) rad(-2) in B- vs. K(χ)≈ 21 kcal mol(-1) rad(-2) in A-DNA-like conformation of 2'-deoxycytidine). Quantum zero-point motion of the nuclei makes the dominant contribution to VRMS deviations of molecules structural parameters: 9-22° for β, ε and P, 5-7° for γ and χ at the temperature of 0 K, and 15-38° for β, ε and P, 9-26° for γ and χ at the room temperature (298.15 K). Obtained results can be used in constructing simple dynamical models of the DNA fragments.

How Flexible are DNA Constituents? The Quantum-Mechanical Study

Relaxed force constants (RFCs) and vibrational root-mean-square deviations have been evaluated by the original calculation method for conformational parameters of the DNA structural units and their constituents: nucleic acid bases (uracile, thymine, cytosine, adenine and guanine) and their ‘building blocks’ (benzene, pyrimidine, imidazole and purine molecules), as well as the DNA backbone structural units: tetrahydrofuran, 1,2-dideoxyribose, methanol and orthophosphoric acid. It has been found that the RFCs for nomenclature torsions β, γ, ε and sugar pseudorotation angle P in 1,2-dideoxyribose are sensible to the molecule conformation and their values are in the range of 1–25 kcal/(mole-rad2) obeying the inequality K γ > K ε > KP > K β. The RFCs values for endocyclic torsions of nucleic acid bases six-member rings lie within 15–45 kcal/(mole·rad2) in pyrimidines and within 20–60 kcal/(mole·rad2) in purines. It is shown that the quantum zero-point motion effectively neglects the amino group non-planarity in cytosine, adenine and partially in guanine.

KINETIC ENERGY DRIVEN SUPERCONDUCTIVITY, THE ORIGIN OF THE MEISSNER EFFECT, AND THE REDUCTIONIST FRONTIER

Is superconductivity associated with a lowering or an increase of the kinetic energy of the charge carriers? Conventional BCS theory predicts that the kinetic energy of carriers increases in the transition from the normal to the superconducting state. However, substantial experimental evidence obtained in recent years indicates that in at least some superconductors the opposite occurs. Motivated in part by these experiments many novel mechanisms of superconductivity have recently been proposed where the transition to superconductivity is associated with a lowering of the kinetic energy of the carriers. However none of these proposed unconventional mechanisms explores the fundamental reason for kinetic energy lowering nor its wider implications. Here I propose that kinetic energy lowering is at the root of the Meissner effect, the most fundamental property of superconductors. The physics can be understood at the level of a single electron atom: kinetic energy lowering and enhanced diamagnetic susceptibility are intimately connected. We propose that this connection extends to superconductors because they are, in a very real sense, "giant atoms". According to the theory of hole superconductivity, superconductors expel negative charge from their interior driven by kinetic energy lowering and in the process expel any magnetic field lines present in their interior. Associated with this we predict the existence of a macroscopic electric field in the interior of superconductors and the existence of macroscopic quantum zero-point motion in the form of a spin current in the ground state of superconductors (spin Meissner effect). In turn, the understanding of the role of kinetic energy lowering in superconductivity suggests a new way to understand the fundamental origin of kinetic energy lowering in quantum mechanics quite generally. This provides a new understanding of "quantum pressure", the stability of matter and the origin of fermion anticommutation relations, it leads to the prediction that spin currents exist in the ground state of aromatic ring molecules, and that the electron wavefunction is double-valued, requiring a reformulation of conventional quantum mechanics.

Back-action-evading measurements of nanomechanical motion

When carrying out ultrasensitive continuous measurements of position, one must ultimately confront the fundamental effects of detection back-action. Back-action forces set a lower bound on the uncertainty in the measured position, the ‘standard quantum limit’ (SQL). Recent measurements of nano- and micromechanical resonators are rapidly approaching this limit. Making measurements with sensitivities surpassing the SQL will require a new kind of approach: back-action-evading (BAE), quantum non-demolition measurement techniques. Here we realize a BAE measurement based on the parametric coupling between a nanomechanical and a microwave resonator. We demonstrate for the first time BAE detection of a single quadrature of motion with sensitivity four times the quantum zero-point motion of the mechanical resonator. We identify a limiting parametric instability inherent in BAE measurement, and describe how to improve the technique to surpass the SQL and permit the formation of squeezed states of motion.

Thermal expansion in single-walled carbon nanotubes and graphene: Nonequilibrium Green’s function approach

The nonequilibrium Green's function method is applied to investigate the coefficient of thermal expansion (CTE) in single-walled carbon nanotubes (SWCNT) and graphene. It is found that atoms expand about 1% from equilibrium positions even at $T=0\text{ }\text{K}$, resulting from the interplay between quantum zero-point motion and nonlinear interaction. The CTE in SWCNT of different sizes is studied and analyzed in terms of the competition between various vibration modes. As a result of this competition, the axial CTE is positive in the whole temperature range, while the radial CTE is negative at low temperatures. In graphene, the CTE is very sensitive to the substrate. Without substrate, CTE has large negative region at low temperatures and very small value at high-temperature limit, and the value of CTE at 300 K is $\ensuremath{-}6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\text{ }{\text{K}}^{\ensuremath{-}1}$ which is very close to a recent experimental result, $\ensuremath{-}7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\text{ }{\text{K}}^{\ensuremath{-}1}$ [Nat. Nanotechnol. 10, 1038 (2009)]. A very weak substrate interaction (about 0.06% of the in-plane interaction) can largely reduce the negative CTE region and greatly enhance the value of CTE. If the substrate interaction is strong enough, the CTE will be positive in whole temperature range and the saturate value at high temperatures reaches $2.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\text{ }{\text{K}}^{\ensuremath{-}1}$.

Electronic states near a quantum fluctuating point vortex in ad-wave superconductor: Dirac fermion theory

We introduce a simple model of the low energy electronic states in the vicinity of a vortex undergoing quantum zero-point motion in a d-wave superconductor. The vortex is treated as a point flux tube, carrying pi-flux of an auxiliary U(1) gauge field, which executes simple harmonic motion in a pinning potential. The nodal Bogoliubov quasiparticles are represented by Dirac fermions with unit U(1) gauge charge. The energy dependence of the local density of electronic states (LDOS) at the vortex center has no zero bias peak; instead, small satellite features appear, driven by transitions between different vortex eigenmodes. These results are qualitatively consistent with scanning tunneling microscopy measurements of the sub-gap LDOS in cuprate superconductors. Furthermore, as argued in L. Balents et al., Phys.Rev.B 71, 144508 (2005), the zero-point vortex motion also leads naturally to the observed periodic modulations in the spatial dependence of the sub-gap LDOS.

Influence of the quantum zero-point motion of a vortex on the electronic spectra ofs-wave superconductors

We compute the influence of the quantum zero-point motion of a vortex on the electronic quasiparticle spectra of s-wave superconductors. The vortex is assumed to be pinned by a harmonic potential, and its coupling to the quasiparticles is computed in the framework of BCS theory. Near the core of the vortex, the motion leads to a shift of spectral weight away from the chemical potential, and thereby reduces the zero bias conductance peak; additional structure at the frequency of the harmonic trap is also observed.

Detecting the quantum zero-point motion of vortices in the cuprate superconductors

We explore the experimental implications of a recent theory of the quantum dynamics of vortices in two-dimensional superfluids proximate to Mott insulators. The theory predicts modulations in the local density of states in the regions over which the vortices execute their quantum zero-point motion. We use the spatial extent of such modulations in scanning tunnelling microscopy measurements [J.E. Hoffman, E.W. Hudson, K.M. Lang, V. Madhavan, S.H. Pan, H. Eisaki, S. Uchida, J.C. Davis, Science 295 (2002) 466] on the vortex lattice of Bi 2Sr 2CaCu 2O 8+ δ to estimate the inertial mass of a point vortex. We discuss other, more direct, experimental signatures of the vortex dynamics.

Quantum atomistic simulations of silicon and germanium

Quantum atomistic simulations of crystalline silicon and germanium have been carried out by the path-integral Monte Carlo method. The interatomic interactions were modeled by Stillinger–Weber-type potentials, with parameters adequate to quantum simulations. Quantum zero-point motion together with anharmonicity of the interatomic potential led to a lattice expansion of 7 × 10−3 Å for both Si and Ge. Results for the equation-of-state (volume versus pressure) and for the thermal expansion coefficient agreed well with experimental results for both materials at T > 100 K and for hydrostatic pressures up to 100 kbar.

Nuclear spin relaxation of powdered metallic antimony in liquid 3He

Nuclear spin relaxation studies have been carried out to determine the surface relaxation of powdered Sb immersed in liquid 3 He. The surface relaxation mechanism was observed to be significantly more effective than the bulk Korringa relaxation rate for temperatures T < 75 mK. This surface relaxation is attributed to the modulation of the dipole-dipole interaction between the Sb spins at the metal surface and the 3 He spins in the solid-like layer on the surface by the quantum zero-point motion of these 3 He atoms. The total relaxation has been analyzed in terms of the surface relaxation and the spin diffusion through the bulk of the Sb particles. The experimental results are in excellent agreement with the theory developed for this system. Replacement of the 3 He by 4 He removes the surface relaxation component and restores the relaxation rates to the bulk value.

Relaxation in Powdered Metallic Antimony in Contact with Liquid 3 He

The nuclear spin-lattice relaxation in finely powdered antimony metal immersed in liquid 3 He has been studied at low temperatures. For T < 75 mK, a new surface relaxation mechanism becomes significant. This surface relaxation is due to the modulation by the quantum zero-point motion of the dipole-dipole interaction between the Sb spins at the metal surface and the 3 He spins in the solid-like layer on the surface. Replacement of the liquid 3 He by 4 He restores the relaxation rates to the bulk value. This work helps explain anomalies found in previous relaxation studies on powdered Pt immersed in liquid 3 He.

On the Quantum Nature of the Shared Proton in Hydrogen Bonds

The relative influence of thermal and quantum fluctuations on the proton transfer properties of the charged water complexes H5O2+ and H3O2- was investigated with the use of ab initio techniques. These small systems can be considered as prototypical representatives of strong and intermediate-strength hydrogen bonds. The shared proton in the strongly hydrogen bonded H5O2+ behaved in an essentially classical manner, whereas in the H3O2- low-barrier hydrogen bond, quantum zero-point motion played a crucial role even at room temperature. This behavior can be traced back to a small difference in the oxygen-oxygen separation and hence to the strength of the hydrogen bond.