arXiv subjects

Yuval Gefen

Publications and source records attributed to Yuval Gefen.

At least 127 records · Page 7Linked to original sources

arXiv2014

Hanbury Brown and Twiss Correlations in Quantum Hall Systems

We study a Hanbury Brown and Twiss (HBT) interferometer formed with chiral edge channels of a quantum Hall system. HBT cross-correlations are calculated for a device operating both in the integer and fractional quantum Hall regimes, the latter at Laughlin filling fractions. We find that in both cases, when the current is dominated by electron tunneling, current-current correlations show antibunching, characteristic of fermionic correlations. When the current-current correlations are dominated by quasiparticle tunneling, the correlations reveal bunching, characteristic of bosons. For electron tunneling we use Keldysh technique, and show that the result for fractional filling factors can be obtained in a simple way from the results of the integer case. It is shown that quasiparticle-dominated cross-current correlations can be analyzed by means of a quantum master equation approach. We present here a detailed derivation of the results of Ref. [Phys. Rev. Lett. 109, 106802 (2012)] and generalize them to all Laughlin fractions.

cond-mat.mes-hall↗

arXiv2013

Edge reconstruction in the $ν=2/3$ fractional quantum Hall state

The edge structure of the $ν=2/3$ fractional quantum Hall state has been studied for several decades but recent experiments, exhibiting upstream neutral mode(s), a plateau at a Hall conductance of $\frac{1}{3}( e^2/h)$ through a quantum point contact, and a crossover of the effective charge, from $e/3$ at high temperature to $2e/3$ at low temperature, could not be explained by a single theory. Here we develop such a theory, based on edge reconstruction due to a confining potential with finite slope, that admits an additional $ν=1/3$ incompressible strip near the edge. Renormalization group analysis of the effective edge theory due to disorder and interactions explains the experimental observations.

cond-mat.str-el↗

arXiv2013

Transmission phase lapses through a quantum dot in a strong magnetic field

The phase of the transmission amplitude through a mesoscopic system contains information about the system's quantum mechanical state and excitations thereof. In the absence of an external magnetic field, abrupt phase lapses occur between transmission resonances of quantum dots and can be related to the signs of tunneling matrix elements. They are smeared at finite temperatures. By contrast, we show here that in the presence of a strong magnetic field, phase lapses represent a genuine interaction effect and may occur also on resonance. For some realistic parameter range these phase lapses are robust against finite temperature broadening.

cond-mat.mes-hall↗

arXiv2013

Null Values and Quantum State Discrimination

We present a measurement protocol for discriminating between two different quantum states of a qubit with high fidelity. The protocol, called null value, is comprised of a projective measurement performed on the system with a small probability (also known as partial-collapse), followed by a tuned postselection. We report on an optical experimental implementation of the scheme. We show that our protocol leads to an amplified signal-to-noise ratio (as compared with a straightforward strong measurement) when discerning between the two quantum states.

quant-ph↗

arXiv2013

Standard and Null Weak Values

Weak value (WV) is a quantum mechanical measurement protocol, proposed by Aharonov, Albert, and Vaidman. It consists of a weak measurement, which is weighed in, conditional on the outcome of a later, strong measurement. Here we define another two-step measurement protocol, null weak value (NVW), and point out its advantages as compared to WV. We present two alternative derivations of NWVs and compare them to the corresponding derivations of WVs.

quant-ph↗

arXiv2013

Null weak values in multi-level systems

A two-step measurement protocol of a quantum system, known as weak value (WV), has been introduced more than two decades ago by Aharonov et al. [1], and has since been studied in various contexts. Here we discuss another two-step measurement protocol which we dub null weak value (NWV). The protocol consists of a partial-collapse measurement followed by quantum manipulation on the system and finally a strong measurement. The first step is a strong measurement which takes place with small probability. The second strong measurement is used as postselection on the outcome of the earlier step. Not being measured in the partial-collapse stage (null outcome) leads to a non-trivial correlation between the two measurements. The NVW protocol, first defined for a two-level system [2], is generalized to a multi-level system, and compared to the standard-WV protocol.

quant-ph↗

arXiv2012

Controlled dephasing of an electron interferometer with a path detector at equilibrium

Controlled dephasing of electrons, via 'which path' detection, involves, in general, coupling a coherent system to a current driven noise source. However, here, we present a case in which a nearly isolated electron puddle at thermal equilibrium strongly affects the coherence of a nearby electronic interferometer. Moreover, for certain average electron occupations of the puddle, the interferometer exhibits complete dephasing. This robust phenomenon stems from the Friedel Sum Rule, which relates a system's occupation with its scattering phases. The interferometer opens a peeping window into physics of the isolated electron puddle, which cannot be accessed otherwise.

cond-mat.mes-hall↗

arXiv2012

A quantum dot close to Stoner instability: the role of Berry's Phase

The physics of a quantum dot with electron-electron interactions is well captured by the so called "Universal Hamiltonian" if the dimensionless conductance of the dot is much higher than unity. Within this scheme interactions are represented by three spatially independent terms which describe the charging energy, the spin-exchange and the interaction in the Cooper channel. In this paper we concentrate on the exchange interaction and generalize the functional bosonization formalism developed earlier for the charging energy. This turned out to be challenging as the effective bosonic action is formulated in terms of a vector field and is non-abelian due to the non-commutativity of the spin operators. Here we develop a geometric approach which is particularly useful in the mesoscopic Stoner regime, i.e., when the strong exchange interaction renders the system close the the Stoner instability. We show that it is sufficient to sum over the adiabatic paths of the bosonic vector field and, for these paths, the crucial role is played by the Berry phase. Using these results we were able to calculate the magnetic susceptibility of the dot. The latter, in close vicinity of the Stoner instability point, matches very well with the exact solution [I.S. Burmistrov, Y. Gefen, M.N. Kiselev, JETP Lett. 92 (2010) 179].

cond-mat.mes-hall↗

arXiv2012

Hanbury-Brown and Twiss interference of anyons

We present a study of an Hanbury Brown and Twiss (HBT) interferometer realized with anyons. Such a device can directly probe entanglement and fractional statistics of initially uncorrelated particles. We calculate HBT cross-correlations of Abelian Laughlin anyons. The correlations we calculate exhibit partial bunching similar to bosons, indicating a substantial statistical transmuta- tion from the underlying electronic degrees of freedom. We also find qualitative differences between the anyonic signal and the corresponding bosonic or fermionic signals, indicating that anyons cannot be simply thought as intermediate between bosons and fermions.

cond-mat.mes-hall↗

arXiv2012

Mesoscopic Stoner instability in metallic nanoparticles revealed by shot noise

We study sequential tunneling through a metallic nanoparticle close to the Stoner instability coupled to parallely magnetized electrodes. Increasing the bias voltage successively opens transport channels associated with excitations of the nanoparticle's total spin. For the current this leads just to a steplike increase. The Fano factor, in contrast, shows oscillations between large super-Poissonian and sub-Poissonian values as a function of bias voltage. We explain the enhanced Fano factor in terms of generalized random-telegraph noise and propose the shot noise as a convenient tool to probe the mesoscopic Stoner instability.

cond-mat.mes-hall↗

arXiv2012

Incoherent scatterer in a Luttinger liquid: a new paradigmatic limit

We address the problem of a Luttinger liquid with a scatterer that allows for both coherent and incoherent scattering channels. The asymptotic behavior at zero temperature is governed by a new stable fixed point: a Goldstone mode dominates the low energy dynamics, leading to a universal behavior. This limit is marked by equal probabilities for forward and backward scattering. Notwithstanding this non-trivial scattering pattern, we find that the shot noise as well as zero cross-current correlations vanish. We thus present a paradigmatic picture of an impurity in the Luttinger model, alternative to the Kane-Fisher picture.

cond-mat.mes-hall↗

arXiv2012

Entanglement entropy and quantum phase transitions in quantum dots coupled to Luttinger liquid wires

We study a quantum phase transition which occurs in a system composed of two impurities (or quantum dots) each coupled to a different interacting (Luttinger-liquid) lead. While the impurities are coupled electrostatically, there is no tunneling between them. Using a mapping of this system onto a Kondo model, we show analytically that the system undergoes a Berezinskii-Kosterlitz-Thouless quantum phase transition as function of the Luttinger liquid parameter in the leads and the dot-lead interaction. The phase with low values of the Luttinger-liquid parameter is characterized by an abrupt switch of the population between the impurities as function of a common applied gate voltage. However, this behavior is hard to verify numerically since one would have to study extremely long systems. Interestingly though, at the transition the entanglement entropy drops from a finite value of $\ln(2)$ to zero. The drop becomes sharp for infinite systems. One can employ finite size scaling to extrapolate the transition point and the behavior in its vicinity from the behavior of the entanglement entropy in moderate size samples. We employ the density matrix renormalization group numerical procedure to calculate the entanglement entropy of systems with lead lengths of up to 480 sites. Using finite size scaling we extract the transition value and show it to be in good agreement with the analytical prediction.

cond-mat.mes-hall↗

arXiv2012

An Exact Solution for Spin and Charge Correlations in Quantum Dots: The Effect of Level Fluctuations and Zeeman Splitting

The inclusion of charging and spin-exchange interactions within the Universal Hamiltonian description of quantum dots is challenging as it leads to a non-Abelian action. Here we present an exact analytical solution of the probem, in particular, in the vicinity of the Stoner instabilty. We calculate the tunneling density of states and the spin susceptibility. We demonstrate that near the Stoner instability the spin susceptibility follows a Curie law with an effective spin. The latter depends logarithmically on temperature due to the statistical fluctuations of the single-particle levels. Near the Stoner instability the tunneling density of states exhibits a non-monotonous behavior as function of the tunneling energy, even at temperatures higher than the exchange energy. This is due to ehnanced spin correlations. Our results could be tested in quantum dots made of nearly ferromagnetic materials.

cond-mat.mes-hall↗

arXiv2011

Zero temperature Dephasing and the Friedel Sum Rule

Detecting the passage of an interfering particle through one of the interferometer's arms, known as "which path" measurement, gives rise to interference visibility degradation (dephasing). Here we consider a detector at {\em equilibrium}. At finite temperature dephasing is caused by thermal fluctuations of the detector. More interestingly, in the zero temperature limit, equilibrium quantum fluctuations of the detector give rise to dephasing of the out-of-equilibrium interferometer. This dephasing is a manifestation of an orthogonality catastrophe which differs qualitatively from Anderson's. Its magnitude is directly related to the Friedel sum rule.

cond-mat.mes-hall↗

arXiv2011

Anderson Orthogonality in the Dynamics After a Local Quantum Quench

We present a systematic study of the role of Anderson orthogonality for the dynamics after a quantum quench in quantum impurity models, using the numerical renormalization group. As shown by Anderson in 1967, the scattering phase shifts of the single-particle wave functions constituting the Fermi sea have to adjust in response to the sudden change in the local parameters of the Hamiltonian, causing the initial and final ground states to be orthogonal. This so-called Anderson orthogonality catastrophe also influences dynamical properties, such as spectral functions. Their low-frequency behaviour shows nontrivial power laws, with exponents that can be understood using a generalization of simple arguments introduced by Hopfield and others for the X-ray edge singularity problem. The goal of this work is to formulate these generalized rules, as well as to numerically illustrate them for quantum quenches in impurity models involving local interactions. As a simple yet instructive example, we use the interacting resonant level model as testing ground for our generalized Hopfield rule. We then analyse a model exhibiting population switching between two dot levels as a function of gate voltage, probed by a local Coulomb interaction with an additional lead serving as charge sensor. We confirm a recent prediction that charge sensing can induce a quantum phase transition for this system, causing the population switch to become abrupt. We elucidate the role of Anderson orthogonality for this effect by explicitly calculating the relevant orthogonality exponents.

cond-mat.str-el↗

arXiv2011

Charge sensing amplification via weak values measurement

A protocol employing weak values (WVs) to obtain ultra sensitive amplification of weak signals in the context of a solid state setup is proposed. We consider an Aharonov-Bohm interferometer where both the orbital and the spin degrees of freedom are weakly affected by the presence of an external charge to be detected. The interplay between the spin and the orbital WVs leads to a significant amplification even in the presence of finite temperature, voltage, and external noise.

cond-mat.mes-hall↗

arXiv2011

Population switching and charge sensing in quantum dots: A case for a quantum phase transition

A broad and a narrow level of a quantum dot connected to two external leads may swap their respective occupancies as a function of an external gate voltage. By mapping this problem onto a multi-flavored Coulomb-gas we show that such population switching is not abrupt. However, trying to measure it by adding a third electrostatically coupled lead may render this switching an abrupt first order quantum phase transition. This is related to the interplay of the Mahan mechanism versus the Anderson orthogonality catastrophe, in similitude to the Fermi edge singularity. A concrete setup for experimental observation of this effect is also suggested.

cond-mat.mes-hall↗

arXiv2010

Non-equilibrium 1D many-body problems and asymptotic properties of Toeplitz determinants

Non-equilibrium bosonization technique facilitates the solution of a number of important many-body problems out of equilibrium, including the Fermi-edge singularity, the tunneling spectroscopy and full counting statistics of interacting fermions forming a Luttinger liquid. We generalize the method to non-equilibrium hard-core bosons (Tonks-Girardeau gas) and establish interrelations between all these problems. The results can be expressed in terms of Fredholm determinants of Toeplitz type. We analyze the long time asymptotics of such determinants, using Szegő and Fisher-Hartwig theorems. Our analysis yields dephasing rates as well as power-law scaling behavior, with exponents depending not only on the interaction strength but also on the non-equilibrium state of the system.

cond-mat.mes-hall↗