Quantum Mechanical Limits Research Articles

Quantum Limits of Covert Target Detection.

In covert target detection, Alice attempts to send optical or microwave probes to determine the presence or absence of a weakly reflecting target embedded in thermal background radiation within a target region, while striving to remain undetected by an adversary, Willie, who is co-located with the target and collects all light that does not return to Alice. We formulate this problem in a realistic setting and derive quantum-mechanical limits on Alice's error probability performance in entanglement-assisted target detection for any fixed level of her detectability by Willie. We demonstrate how Alice can approach this performance limit using two-mode squeezed vacuum probes in the regime of small to moderate background brightness, and how such protocols can outperform any conventional approach using Gaussian-distributed coherent states. In addition, we derive a universal performance bound for nonadversarial quantum illumination without requiring the passive-signature assumption.

Einstein-Rosen bridge from the minimal length

We use a string T-duality corrected pair of regular black holes to construct an Einstein-Rosen (ER) bridge with the wormhole throat proportional to the zero-point (Planck) length. This may be a geometric realization of quantum entanglement for particle/antiparticle pairs. We point out that for an extreme mass configuration consisting of a black hole pair, one can have an ER bridge with a horizon area that coincides with the Bekenstein minimal area bound along with a wormhole mass proportional to the Planck mass. This could be related to gravitational self-completeness with quantum mechanical mass limits. We also discuss the ER bridge for sub-Planckian mass horizonless wormholes and show this admits a region of negative energy at the throat, which we posit to be related to a particle of negative mass generated by quantum fluctuations or the Casimir effect. We argue that Hawking radiation could be the best way for the geometric realization of quantum entanglement for particle/antiparticle pairs emitted by black holes. This sheds new light on the ER=EPR conjecture.

Dispersive interactions between standard and Dirac materials and the role of dimensionality

The van der Waals (vdW) interaction plays a prominent role between neutral objects at separations where short ranged chemical forces are negligible. This type of dispersive coupling is determined by the interplay between geometry and response properties of the materials making up the objects. Here, we investigate the vdW interaction between 1D, 2D, and 3D standard and Dirac materials within the Random Phase Approximation, which takes into account collective excitations originating from the electronic Coulomb potential. A comprehensive understanding of characteristic functionalities and scaling laws are obtained for systems with parabolic energy dispersion (standard materials) and crossing linear bands (Dirac materials). By comparing the quantum mechanical and thermal limits the onset of thermal fluctuations in the vdW interaction is discussed showing that thermal effects are significantly pronounced at smaller scales in reduced dimensions.

Special Issue on Optical In-Process Measurement Systems

Optical principles enable precise measurements, down to the quantum mechanical limits, and provide the fastest possible measurement speed: the speed of light [...]

Gravitation, Density, Black Holes and Spatial Quantization

Making use of Newton’s classical shell theorem, the Schwarzschild metric is modified. This removes the singularity at r = 0 for a standard object (not a black hole). It is demonstrated how general relativity evidently leads to quantization of space-time. Both classical and quantum mechanical limits on density give the same result. Based on Planck’s length and the assumption that density must have an upper limit, we conclude that the lower limit of the classical gravitation theory by Einstein is related to the Planck length, which is a quantum phenomenon posed by dimensional analysis of the universal constants. The Ricci tensor is considered under extreme densities (where Kretschmann invariant = 0) and a solution is considered for both outside and inside the object. Therefore, classical relativity and the relationship between the universal constants lead to quantization of space. A gedanken experiment of light passing through an extremely dense object is considered, which will allow for evaluation of the theory.

On the Order Parameter of the Continuous Phase Transition in the Classical and Quantum Mechanical Limits

The mean field theory is revisited in the classical and quantum mechanical limits. Taking into account the boundary conditions at the phase transition and the third law of the thermodynamics the physical properties of the ordered and disordered phases were reported. The equation for the order parameter predicts the occurrence of a saturation of $\Psi^2$ = 1 near $\Theta_S$, the temperature below the quantum mechanical ground state is reached. The theoretical predictions are also compared with high resolution thermal expansion data of SrTiO$_{\text{3}}$ monocrystalline samples and other some previous results. An excellent agreement has been found suggesting a universal behavior of the theoretical model to describe continuous structural phase transitions.

Carbon Nanotubes-Based Digitally Programmable Current Follower

The physical constraints of ever-shrinking CMOS transistors are rapidly approaching atomistic and quantum mechanical limits. Therefore, research is now directed towards the development of nanoscale devices that could work efficiently in the sub-10 nm regime. This coupled with the fact that recent design trend for analog signal processing applications is moving towards current-mode circuits which offer lower voltage swings, higher bandwidth, and better signal linearity is the motivation for this work. A digitally controlled DVCC has been realized using CNFETs. This work exploited the CNFET’s parameters like chirality, pitch, and numbers of CNTs to perform the digital control operation. The circuit has minimum number of transistors and can control the output current digitally. A similar CMOS circuit with 32 nm CMOS parameters was also simulated and compared. The result shows that CMOS-based circuit requires 418.6 μW while CNFET-based circuit consumes 352.1 μW only. Further, the proposed circuit is used to realize a CNFET-based instrumentation amplifier with digitally programmable gain. The amplifier has a CMRR of 100 dB and ICMR equal to 0.806 V. The 3 dB bandwidth of the amplifier is 11.78 GHz which is suitable for the applications like navigation, radar instrumentation, and high-frequency signal amplification and conditioning.

Ratchet effect in graphene with trigonal clusters

In this study, we explore the ratchet effect in graphene with artificial, triangular scatterers from a theoretical standpoint. It is demonstrated that the skew scattering of carriers by such coherently oriented defects results in the ratchet effect in graphene, i.e., in a direct current under the action of an oscillating electric field. Scattering on various types of defects exhibiting threefold symmetry is considered in this paper: scattering on a cluster in the shape of a solid triangle in the classical and quantum mechanical limits, and scattering on three-point defects placed at the corners of a triangle. The DC current is calculated for a classical range of oscillating field frequencies.

Quantum limits of interferometer topologies for gravitational radiation detection

In order to expand the astrophysical reach of gravitational wave (GW) detectors, several interferometer topologies have been proposed, in the past, to evade the thermodynamic and quantum mechanical limits in future detectors. In this work, we make a systematic comparison among these topologies by considering their sensitivities and complexities. We numerically optimize their sensitivities by introducing a cost function that tries to maximize the broadband improvement over the sensitivity of current detectors. We find that frequency-dependent squeezed-light injection with a 100 m scale filter cavity yields a good broadband sensitivity, with low complexity, and good robustness against optical loss. This study gives us a guideline for the near-term experimental research programs in enhancing the performance of future GW detectors.

Self-sustained oscillations of a torsional SQUID resonator induced by Lorentz-force back-action

For the study of nanomechanical resonators, ultra-sensitive measurement techniques are crucial. However, if the measurement sensitivity approaches quantum-mechanical limits, the back-action of the detector on the resonator cannot be neglected. If the back-action is strong enough, the corresponding instability can create self-sustained oscillators in the resonator. Here we demonstrate that a torsional mechanical resonator, which contains a direct current SQUID displacement detector, leads to this effect. We find that the Lorentz-force back-action can be so large that, in combination with complex nonlinear Josephson dynamics, it generates intrinsic self-sustained oscillations. The flux quantization limit of the maximum oscillation amplitude is exploited to calibrate the displacement resolution, which is shown to be below the standard quantum limit. The suspended torsional SQUID provides an interesting platform to study on-chip laser-like physics in an electromechanical system that can be controlled by both a flux and current bias.

Coexistence of High-Bit-Rate Quantum Key Distribution and Data on Optical Fiber

Quantum key distribution (QKD) uniquely allows distribution of cryptographic keys with security verified by quantum mechanical limits. Both protocol execution and subsequent applications require the assistance of classical data communication channels. While using separate fibers is one option, it is economically more viable if data and quantum signals are simultaneously transmitted through a single fiber. However, noise-photon contamination arising from the intense data signal has severely restricted both the QKD distances and secure key rates. Here, we exploit a novel temporal-filtering effect for noise-photon rejection. This allows high-bit-rate QKD over fibers up to 90 km in length and populated with error-free bidirectional Gb/s data communications. With high-bit rate and range sufficient for important information infrastructures, such as smart cities and 10 Gbit Ethernet, QKD is a significant step closer towards wide-scale deployment in fiber networks.

Local probing of propagating acoustic waves in a gigahertz echo chamber

In the same way that micro-mechanical resonators resemble guitar strings and drums, Surface Acoustic Waves (SAW) resemble the sound these instruments produce, but moving over a solid surface rather than through air. In contrast with oscillations in suspended resonators, such propagating mechanical waves have not before been studied near the quantum mechanical limits. Here, we demonstrate local probing of SAW with a displacement sensitivity of 30amRMS/sqrt(Hz) and detection sensitivity on the single-phonon level after averaging, at a frequency of 932MHz. Our probe is a piezoelectrically coupled Single Electron Transistor, which is sufficiently fast, non-destructive and localized to let us track pulses echoing back and forth in a long acoustic cavity, self-interfering and ringing the cavity up and down. We project that strong coupling to quantum circuits will allow new experiments, and hybrids utilizing the unique features of SAW. Prospects include quantum investigations of phonon-phonon interactions, and acoustic coupling to superconducting qubits, for which we present favourable estimates.

Quantum mechanical limits to the control of atom–diatom chemical reactions through the polarisation of the reactants

This article considers the extent to which one can control the reactivity of atom-diatom systems through reactant polarisation. Three different limits for reactivity manipulation are defined: "absolute" limits that do not depend on the reaction dynamics but can only be obtained for particular combinations of quantum numbers, "unconstrained" limits that depend on dynamics but not on constraints imposed by any particular experimental setup, and "constrained" limits that depend on dynamics and also on the constraints imposed by a particular experimental setup. Methods for calculation of these limits are presented and applied to the benchmark F + H2 reaction. The variations of the maximum and minimum reactivity one can obtain are analysed in terms of reaction mechanisms and steric constraints. Tables listing the minimum and maximum values of angular momentum polarisation moments of rank up to 4, and integer and half-integer quantum numbers up to 5, are also presented.

Quantum-noise theory for terahertz hot electron bolometer mixers

In this paper, we first review general quantum mechanical limits on the sensitivity of heterodyne receivers. The main aim of the paper is to explore the quantum-noise (QN) properties of hot electron bolometric (HEB) mixers. HEB mixers have a characteristic feature not found in other mixers: based on the "hot-spot" model, the conversion loss varies along the length dimension of the bolometer, and some sections of the bolometer are essentially passive, in which little frequency conversion occurs. We analyze a quantitative distributed quantum-noise model of the HEB mixer, making use of simulated hot-spot model data, that takes into account the continuous variation of the sensitivity along the bolometer bridge. An expression for the HEB receiver noise temperature, including optical input loss, is derived. We find that the predicted double-sideband receiver noise temperature agrees well with the available measured data (up to 5.3 THz). The results of our analysis suggest that QN and classical HEB noise contribute about equally at 3 THz, while at higher terahertz frequencies QN dominates. QN thus appears to show measurable effects in existing HEB mixers and will be even more important to take into account as HEB mixers continue to be developed for higher terahertz frequencies.

Putting Mechanics into Quantum Mechanics

Nanoelectromechanical structures are starting to approach the ultimate quantum mechanical limits for detecting and exciting motion at the nanoscale. Nonclassical states of a mechanical resonator are also on the horizon.

Scattering theory of plasmon-assisted entanglement transfer and distillation

We analyze the quantum-mechanical limits to the plasmon-assisted entanglement transfer observed by Altewischer, van Exter, and Woerdman [Nature 418, 304 (2002)]. The maximal violation S of Bell's inequality at the photodetectors behind two linear media (such as the perforated metal films in the experiment) can be described by two ratio's ${\ensuremath{\tau}}_{1},$ ${\ensuremath{\tau}}_{2}$ of polarization-dependent transmission probabilities. A fully entangled incident state is transferred without degradation for ${\ensuremath{\tau}}_{1}={\ensuremath{\tau}}_{2},$ but a relatively large mismatch of ${\ensuremath{\tau}}_{1}$ and ${\ensuremath{\tau}}_{2}$ can be tolerated with a small reduction of S. We predict that fully entangled Bell pairs can be distilled out of partially entangled radiation if ${\ensuremath{\tau}}_{1}$ and ${\ensuremath{\tau}}_{2}$ satisfy a pair of inequalities.

Information Localization in the Electron Microscope

Historically, the resolution achievable in an electron microscope has been limited by the unavoidable aberrations of the lenses used to form the image [1]. However recently, aberration correctors have been shown to be able to improve both the ultimate resolution attainable, and the current available to form the image at any given resolution [2]. The resolution in aberration corrected instruments will soon approach the quantum mechanical limits, and we investigate how these limits depend on the imaging mode used.

Transport via a quantum shuttle

We present preliminary results for a model of electron transport through an electromechanical system in the extreme quantum mechanical and Coulomb blockade limits. The system consists of three quantum dots in which the outer dots are fixed and the central dot is mounted on a quantum harmonic oscillator, thus forming a quantum shuttle. The current through the system as a function of the energy level shift between the outer dots has marked resonances which are associated with avoided level-crossings in the eigenvalue spectrum.

Theory of Photon-Assisted Tunneling in the Transition between the Quantum Mechanical and Classical Limits

We report unpublished experimental results of Photon-Assisted Tunneling (PAT) in the transition region between the quantum mechanical and classical limits. Using these results, we show that there is a discrepancy between the Tien-Gordon theory of Quasiparticle Photon-Assisted Tunneling and experiment in this region. Finally, we show that the modified Tien-Gordon theory is also valid in this region.

Theory of Photon-Assisted Tunneling in the Transition between the Quantum Mechanical and Classical Limits

We report unpublished experimental results of Photon-Assisted Tunneling (PAT) in the transition region between the quantum mechanical and classical limits. Using these results, we show that there is a discrepancy between the Tien-Gordon theory of Quasiparticle Photon-Assisted Tunneling and experiment in this region. Finally, we show that the modified Tien-Gordon theory is also valid in this region.