Unity Probability Research Articles

Control of reactive collisions by quantum interference.

In this study, we achieved magnetic control of reactive scattering in an ultracold mixture of 23Na atoms and 23Na6Li molecules. In most molecular collisions, particles react or are lost near short range with unity probability, leading to the so-called universal rate. By contrast, the Na + NaLi system was shown to have only ~4% loss probability in a fully spin-polarized state. By controlling the phase of the scattering wave function via a Feshbach resonance, we modified the loss rate by more than a factor of 100, from far below to far above the universal limit. The results are explained in analogy with an optical Fabry-Perot resonator by interference of reflections at short and long range. Our work demonstrates quantum control of chemistry by magnetic fields with the full dynamic range predicted by our models.

Detection of NaRb Feshbach molecules by photodissociation

We demonstrate detection of NaRb Feshbach molecules at high magnetic field by combining molecular photodissociation and absorption imaging of the photofragments. The photodissociation process is carried out via a spectroscopically selected hyperfine Zeeman level correlated with the Na ($3P_{3/2}$) + Rb ($5S_{1/2}$) asymptote which, following spontaneous emission and optical pumping, leads to ground-state atoms in a single level with near unity probability. Subsequent to the dissociation, the number of molecules is obtained by detecting the resultant $^{23}$Na and $^{87}$Rb atoms. We have also studied the heating effect caused by the photodissociation process and optimized the detection protocol for extracting the temperature of the molecular cloud. This method enables the $in~situ$ detection of fast time scale collision dynamics between NaRb Feshbach molecules and will be a valuable capability in studying few-body physics involving molecules.

Fundamental Limits of Quantum-Secure Covert Communication Over Bosonic Channels

We investigate the fundamental limit of quantum-secure covert communication over the lossy thermal noise bosonic channel, the quantum-mechanical model underlying many practical channels. We assume that the adversary has unlimited quantum information processing capabilities as well as access to all transmitted photons that do not reach the legitimate receiver. Given existence of noise that is uncontrolled by the adversary, the square root law (SRL) governs covert communication: up to $c\sqrt {n}$ covert bits can be transmitted reliably in $n$ channel uses. Attempting to surpass this limit results in detection with unity probability as $n\rightarrow \infty $ . Here we present the expression for $c$ , characterizing the SRL for the bosonic channel. We also prove that discrete-valued coherent state quadrature phase shift keying (QPSK) constellation achieves the optimal $c$ , which is the same as that achieved by a circularly-symmetric complex-valued Gaussian prior on coherent state amplitude. Finally, while binary phase shift keying (BPSK) achieves the Holevo capacity for non-covert bosonic channels in the low received signal-to-noise ratio regime, we show that it is strictly sub-optimal for covert communication.

Efficient representation of Gaussian states for multimode non-Gaussian quantum state engineering via subtraction of arbitrary number of photons

We introduce a complete description of a multi-mode bosonic quantum state in the coherent-state basis (which in this work is denoted as "$K$" function ), which---up to a phase---is the square root of the well-known Husimi "$Q$" representation. We express the $K$ function of any $N$-mode Gaussian state as a function of its covariance matrix and displacement vector, and also that of a general continuous-variable cluster state in terms of the modal squeezing and graph topology of the cluster. This formalism lets us characterize the non Gaussian state left over when one measures a subset of modes of a Gaussian state using photon number resolving detection, the fidelity of the obtained non-Gaussian state with any target state, and the associated heralding probability, all analytically. We show that this probability can be expressed as a Hafnian, re-interpreting the output state of a circuit claimed to demonstrate quantum supremacy termed Gaussian boson sampling. As an example-application of our formalism, we propose a method to prepare a two-mode coherent-cat-basis Bell state with fidelity close to unity and success probability that is fundamentally higher than that of a well-known scheme that splits an approximate single-mode cat state---obtained by photon number subtraction on a squeezed vacuum mode---on a balanced beam splitter. This formalism could enable exploration of efficient generation of cat-basis entangled states, which are known to be useful for quantum error correction against photon loss.

Model-Free Observation of Polypeptide Translocation Success Rate through a Nanopore

Elucidating the motion of uniformly charged polymers in voltage-biased nanoscale channels has been a scientifically and technologically fruitful enterprise. Non-uniformly charged polymers such as polypeptides present a new set of challenges and opportunities, as they do not in general move through a nanopore unidirectionally or translocate the channel-containing membrane with unity probability. Here we demonstrate a single-molecule, model-free experimental technique to track the motion of a polypeptide in a channel and determine whether each polypeptide ultimately translocates through, or retracts from, the channel. The technique relies on the heterogeneity of the charge density along the polypeptide and its effect on the selectivity of the channel. In a nanopore under an electrolyte concentration gradient, the modulation of the channel selectivity is observable in real time as a change in the ionic conductance. For a polypeptide with different charge densities at the N- and C-termini, the ionic current at the end of a single molecule capture “event” reports on which end of the molecule exits the nanopore, and hence the direction of escape. As a demonstration, we report experimental observations of the interaction of a “diblock copolymer”-like neuronal intrinsically disordered protein, α-synuclein, with mitochondrial voltage-dependent anion channel (VDAC). The voltage-dependent translocation probability derived from the experiments shows that α-synuclein is bound to membrane surfaces with a distribution of binding energies that strongly depends on lipid species. These results have broad general implications for the interactions of peripheral proteins with lipid membranes.

Injection of a single electron from static to moving quantum dots

We study the injection mechanism of a single electron from a static quantum dot into a moving quantum dot. The moving quantum dots are created with surface acoustic waves (SAWs) in a long depleted channel. We demonstrate that the injection process is characterized by an activation law with a threshold that depends on the SAW amplitude and on the dot-channel potential gradient. By sufficiently increasing the SAW modulation amplitude, we can reach a regime where the transfer has unity probability and is potentially adiabatic. This study points to the relevant regime to use moving dots in quantum information protocols.

Electronic transient spectroscopy from the deep UV to the NIR: unambiguous disentanglement of complex processes

Complex multi-stage relaxation and reaction pathways after the optical excitation of molecules makes the disentanglement of the underlying mechanisms challenging. We present four examples that a new transient spectrometer with excitation fully tunable from the deep UV to the IR and 225 to 1700 nm probing allows for an analysis with greatly reduced ambiguity. The temporal resolution of about 50 fs allows us to resolve all relevant processes. For each example there is a new twist in the sequence of relaxation steps that had previously been overlooked. In malachite green it appears that the importance of the phenyl twisting has been overemphasized and rather a charge transfer state should be considered. In TINUVIN-P the predicted twisting as the driving motion for the ultrafast IC is confirmed and leads to a resolution of the earlier puzzle that the sub-5 ps regime shows kinetics deviating from a pure cooling process despite the sub-ps proton transfer cycle. For the bond cleavage of Ph2CH-Cl and Ph2CH-Br the degree of electron transfer within the radical pair can now be determined quantitatively and leads to a profound understanding of the long-term cation yield. For the first time coherent wavepacket motion in the photoproducts is reported. Last but not least the measurement of the GSB recovery in the deep UV allows for the surprising result, that even after S2 excitation of cyclopentenones the triplet states are reached with near unity probability within a few picoseconds.

Complete Bell-state and Greenberger–Horne–Zeilinger-state nondestructive detection based on simplified symmetry analyzer

We present a simplified symmetry analyzer (SA) with cross-Kerr nonlinearity, quantum non-demolition photon number measurement and basic optical elements. Based on the present symmetry analyzer (SA), all the Bell states can be discriminated nondestructively with nearly unity probability. In addition, with the help of cross-phase modulation (XPM) induced by giant cross-Kerr nonlinearity, three-photon Greenberger–Horne–Zeilinger (GHZ) state can also be discriminated determinately and nondestructively, which is supposed to be meaningful in quantum information processing.

Two-way protocols for quantum cryptography with a nonmaximally entangled qubit pair

This paper proposes a scheme for quantum cryptography with a nonmaximally entangled qubit pair. In a two-way configuration similar to quantum super dense coding, a two-bit key can be distributed by a round trip of one particle of the qubit pair and received by an appropriate joint measurement with the other. The security of our scheme is based on the quantum-mechanical impossibility of local unitary transformation between certain nonmaximally entangled states. Although an eavesdropper, Eve, can always identify the quantum state and intercept the key, it is impossible for her to resend the state with a unity probability and the legitimate parties inevitably detect her. Our protocol is also capable to quantum secure direct communication.

Exciton Storage by Mn2+ in Colloidal Mn2+-Doped CdSe Quantum Dots

Colloidal Mn (2+)-doped CdSe quantum dots showing long excitonic photoluminescence decay times of up to tau exc = 15 mus at temperatures over 100 K are described. These decay times exceed those of undoped CdSe quantum dots by approximately 10 (3) and are shown to arise from the creation of excitons by back energy transfer from excited Mn (2+) dopant ions. A kinetic model describing thermal equilibrium between Mn (2+ 4)T 1 and CdSe excitonic excited states reproduces the experimental observations and reveals that, for some quantum dots, excitons can emit with near unity probability despite being approximately 100 meV above the Mn (2+ 4)T 1 state. The effect of Mn (2+) doping on CdSe quantum dot luminescence at high temperatures is thus completely opposite from that at low temperatures described previously.

Frequency-Doubled Fiber Lasers for RF Spectrum Analysis in Spectral-Hole-Burning Media

We demonstrate an RF spectrum analyzer based on spectral-hole burning (SHB) that operates with unity probability of intercept and resolution under 100 kHz. An SHB crystal, which consists of rare-earth ions doped into a crystal host, records the power spectrum of an RF signal modulated onto an optical carrier as a series of spectral holes that persist for about 10 ms. While the crystal's homogeneous and inhomogeneous linewidths place the fundamental limits on resolution and bandwidth, respectively, the practical limits depend on the lasers used to interrogate the record stored in the crystal's absorption profile. Up to now, SHB spectrum analyzers have used chirped beams from externally modulated, stabilized lasers, which have linewidths of under 10 kHz but cannot chirp over much more than octave bandwidths, or directly modulated diode lasers, which can chirp over more than 20GHz but have linewidths of about 1 MHz. Switching to chirped fiber lasers, which have natural linewidths of under 2 kHz and chirping linewidths on the order of 10 kHz, produces a measurement with fine resolution without any laser stabilization. In addition, by chirping the fiber laser with a sufficiently fast piezo, the resulting chirp could extend over tens of gigahertz in under 10 ms, yielding both fine resolution and broad bandwidth without extraordinary stabilization schemes.

Remote interactions between two d -dimensional distributed quantum systems: nonlocal generalized quantum control-NOT gate and entanglement swapping

We present a systematic simple method to implement a generalized quantum control-NOT (CNOT) gate on two d-dimensional distributed systems. First, we show how the nonlocal generalized quantum CNOT gate can be implemented with unity fidelity and unity probability by using a maximally entangled pair of qudits as a quantum channel. We also put forward a scheme for probabilistically implementing the nonlocal operation with unity fidelity by employing a partially entangled qudit pair as a quantum channel. Analysis of the scheme indicates that the use of partially entangled quantum channel for implementing the nonlocal generalized quantum CNOT gate leads to the problem of 'the general optimal information extraction'. We also point out that the nonlocal generalized quantum CNOT gate can be used in the entanglement swapping between particles belonging to distant users in a communication network and distributed quantum computer.

Decision analysis

As teachers of decision analysis, we are delighted to see a prominent clinician such as Dr Yentis embrace the technique as but one of many tools at our disposal [1]. A good mechanic has many tools in his or her garage. Likewise, doctors should have many tools at their disposal for resolving clinical issues. We have found Dr Yentis' analysis of the clinical problems very enlightening. One of the many benefits of performing decision analysis, as Dr Yentis points out, is that it forces clinicians to educate themselves on all the pertinent issues Sometimes, one may be surprised at one's knowledge gap and that one's gut feeling is not quite so accurate if one looks at all the available data objectively. Even though doctors decision-analyse every day in a way described by Dr Yentis, many have not accepted decision analysis as a tool. This is often due not to a lack of enlightenment, but a fear of things that are highly mathematical. Any ‘bug’ in a decision tree would render it inaccurate or impossible to analyse, and would not be helpful to someone trying to understand it. In that context, we wish to point out respectfully that there are some serious and fundamental construction errors in Dr Yentis' decision trees. One of the cardinal rules of an expected value decision tree is that the probabilities of each chance node must add up to unity (probability coherence). This is not the case in any of the decision trees in Dr Yentis' article (probability incoherence should be reserved for modelling a population whose size is changing). We have reconstructed two versions of the decision tree of the tumour example without altering any of the outcomes and utilities (1, 2). For example, in Fig. 1, the chance of surviving after drug treatment with renal failure remains at 70% × 42.9% = 30%. The same idea should apply to the two obstetric problems in the paper. Decision tree for a patient with a hypothetical tumour. The sum of all probabilities from each chance node equals unity. The same decision tree as in Figure 1 with slightly different architecture. The sum of all probabilities from each chance node again equals unity.

Universal Greenberger-Horne-Zeilinger-state analyzer based on two-photon polarization parity detection

We present a universal analyzer for the three-particle Greenberger-Horne-Zeilinger (GHZ) states with quantum nondemolition parity detectors and linear-optics elements. In our scheme, all of the three-photon GHZ states can be discriminated with nearly unity probability in the regime of weak nonlinearity feasible at the present state of the art experimentally. We also show that our scheme can be easily extended to the analysis of the multi-particle GHZ states.

Scheme for Generation of Entanglement among Bimodal Cavities

We present a scheme for generation of an entangled state in manyspatially separated bimodal cavity modes via cavity quantumelectrodynamics. A V-type three-level atom, initially prepared in acoherent superposition of its excited states, successively passesthrough both the bimodal cavities. If the atom is measured in its ground stateafter leaving the last cavity, an entangled state of many cavity modescan be generated. The conditions to generate the maximally entangledstate with unity probability are worked out.

Dissociative adsorption and hydrodechlorination of CCl4 on Ir(1 1 0)

The dissociative adsorption and hydrodechlorination of CCl4 on a single crystal Ir(1 1 0) was investigated using temperature programmed desorption (TPD) and molecular beam techniques. In order to better understand the behavior of CCl4, the adsorption and reactivity of less chlorinated methanes are compared to that of CCl4. CCl4 dissociates on the clean surface with near unity probability at low surface temperatures and decreases very slightly with increasing surface temperature. CHCl3, CH2Cl2, and CH3Cl also dissociate on the clean surface with near unity probability at low surface temperatures, however, the adsorption probability of these molecules are more sensitive to the surface temperature. As the molecule becomes less chlorinated, the adsorption probability falls more rapidly with increasing surface temperature. The preadsorption of hydrogen does not significantly affect the adsorption probability of CCl4 or CHCl3. However, with the β2 adsorption state of hydrogen saturated, CH2Cl2 and CH3Cl dissociatively adsorb with a small probability. Adsorption of CCl4 on the hydrogen precovered surface was found to produce mainly CHCl3 with trace amounts of CH2Cl2 and CH4 (detected as CD4). Similarly, adsorbed CHCl3 will hydrodechlorinate to mainly CH2Cl2. Hydrodechlorination of CCl4 is favored at lower surface temperatures and at higher surface coverages of dissociatively adsorbed CCl4.

Heterogeneous reactions in aircraft gas turbine engines

[1] One-dimensional flow models and unity probability heterogeneous rate parameters are used to estimate the maximum effect of heterogeneous reactions on trace species evolution in aircraft gas turbines. The analysis includes reactions on soot particulates and turbine/nozzle material surfaces. Results for a representative advanced subsonic engine indicate the net change in reactant mixing ratios due to heterogeneous reactions is <10−6 for O2, CO2, and H2O, and <10−10 for minor combustion products such as SO2 and NO2. The change in the mixing ratios relative to the initial values is <0.01%. Since these estimates are based on heterogeneous reaction probabilities of unity, the actual changes will be even lower. Thus, heterogeneous chemistry within the engine cannot explain the high conversion of SO2 to SO3 which some wake models require to explain the observed levels of volatile aerosols. Furthermore, turbine heterogeneous processes will not effect exhaust NOx or NOy levels.

Reactive and Nonreactive Quenching of OH(A 2Σ+) in Collisions with H Atoms

We use trajectory surface hopping methods to calculate cross sections and rate coefficients for reactive and nonreactive quenching of OH(A 2Σ+) in collisions with H atoms. All calculations are based on multireference configuration interaction potential surfaces for the 11A‘ and 21A‘ surfaces of water, using a diabatic representation to describe electronic transitions. The overall rate of quenching plus reaction is in good agreement (lower by 25−30%) with earlier estimates at 300 and 1500 K. Analysis of the trajectories shows that this rate is dominated by a capture mechanism on the 21A‘ state of water, with a nearly unity probability for hopping to the 11A‘ state following formation of a short-lived collision complex. Both reactive and nonreactive decay of the complex are significant, with branching to H + OH (nonreactive quenching), H + OH (atom exchange with quenching), and O(1D) + H2 (reaction) accounting for approximately 45%, 35%, and 20%, respectively, of the product yield. The cross section for ato...

Reactions of gas-phase atomic hydrogen and deuterium with chemically modified Ir(111) surfaces

The reactions of gas-phase atomic hydrogen (H(g)) and deuterium (D(g)) with the chemically modified Ir(111)–p(1×2)-O, and deuterium (D(a)) and hydrogen (H(a)) adatom precovered Ir(111) surfaces at 100 K have been studied using thermal desorption mass spectrometry. Although the Ir(111)–p(1×2)-O surface at a temperature of 100 K is passivated with respect to adsorption of gas-phase H2 and D2, the interaction of H(g) and D(g) with this surface at 100 K results in the subsequent desorption of water in thermal desorption spectra. These results suggest that while the dissociative chemisorption of molecular hydrogen on Ir(111) is precluded by the presence of the (1×2)-O oxygen overlayer, energetically “hot” H(g) reacts readily with this oxygen-modified surface. Moreover, a strong kinetic isotope effect has been observed in the interaction of H(g) and D(g) with D(a) and H(a) precovered Ir(111) surfaces at 100 K. We find that H(a) is more readily replaced by D(g) (abstraction cross section of σD(g)=4.7±0.4×10−16 cm2) than is D(a) by H(g) (σH(g)=2.6±0.2×10−16 cm2). These calculated cross sections assume a unity probability for reaction of H(g) and D(g) with the Ir(111)–p(1×2)-O surface. This observed isotopic difference in abstraction cross sections is consistent with the differences associated with the expected zero point energy of the transition state for the abstraction reaction and differences associated with the zero point energy between H and D adatoms.

Oxidation of GaAs(110) with NO2: A molecular beam study

We describe time-resolved modulated molecular beam measurements of the adsorption of NO2 on the GaAs(110) surface. These measurements provide a quantitative description of the gas–surface interaction; thermal NO2 has a nearly unity sticking probability, dissociating to form NO (which quickly desorbs) and a surface oxide of ∼1/3 ML saturation coverage. The NO2 dissociation probability is strongly controlled by the defect density, the oxygen coverage, and the surface temperature. We have characterized the competition between the processes leading to oxygen deposition, i.e., desorption and diffusion of NO 2 to reactive defects. The barrier energies Ediff=6±2 kcal/mol and Edes=9±2 kcal/mol provide an interesting example of the transition from defect-dominated surface chemistry, typical of low Miller index metal surfaces to defect- insensitive diffusion-limited chemistry, which we argue is generic to corrugated semiconductor surfaces.