Blind Witnesses Quench Quantum Interference without Transfer of Which-Path Information.

Quantum computation is often limited by environmentally-induced decoherence. We examine the loss of coherence for a two-branch quantum interference device in the presence of multiple witnesses, representing an idealized environment. Interference oscillations are visible in the output as the magnetic flux through the branches is varied. Quantum double-dot witnesses are field-coupled and symmetrically attached to each branch. The global system-device and witnesses-undergoes unitary time evolution with no increase in entropy. Witness states entangle with the device state, but for these blind witnesses, which-path information is not able to be transferred to the quantum state of witnesses-they cannot "see" or make a record of which branch is traversed. The system which-path information leaves no imprint on the environment. Yet, the presence of a multiplicity of witnesses rapidly quenches quantum interference.

Quantum operator entropies under unitary evolution.

For a quantum state undergoing unitary Schrödinger time evolution, the von Neumann entropy is constant. Yet the second law of thermodynamics, and our experience, show that entropy increases with time. Ingarden introduced the quantum operator entropy, which is the Shannon entropy of the probability distribution for the eigenvalues of a Hermitian operator [R. S. Ingarden, Quantum information theory, Rep. Math. Phys. 10, 43 (1976)RMHPBE0034-487710.1016/0034-4877(76)90005-7]. These entropies characterize the missing information about a particular observable inherent in the quantum state itself. The von Neumann entropy is the quantum operator entropy for the case when the operator is the density matrix. We examine pure state unitary evolution in a simple model system composed of a set of highly interconnected topologically disordered states and a time-independent Hamiltonian. An initially confined state is subject to free expansion into available states. The time development is completely reversible with no loss of quantum information and no course graining is applied. The positional entropy increases in time in a way that is consistent with both the classical statistical mechanical entropy and the second law.

Entanglement loss in molecular quantum-dot qubits due to interaction with the environment.

We study quantum entanglement loss due to environmental interaction in a condensed matter system with a complex geometry relevant to recent proposals for computing with single electrons at the nanoscale. We consider a system consisting of two qubits, each realized by an electron in a double quantum dot, which are initially in an entangled Bell state. The qubits are widely separated and each interacts with its own environment. The environment for each is modeled by surrounding double quantum dots placed at random positions with random orientations. We calculate the unitary evolution of the joint system and environment. The global state remains pure throughout. We examine the time dependence of the expectation value of the bipartite Clauser-Horne-Shimony-Holt (CHSH) and Brukner-Paunkovic-Rudolph-Vedral (BPRV) Bell operators and explore the emergence of correlations consistent with local realism. Though the details of this transition depend on the specific environmental geometry, we show how the results can be mapped on to a universal behavior with appropriate scaling. We determine the relevant disentanglement times based on realistic physical parameters for molecular double-dots.

Electric-field-driven electron-transfer in mixed-valence molecules.

Molecular quantum-dot cellular automata is a computing paradigm in which digital information is encoded by the charge configuration of a mixed-valence molecule. General-purpose computing can be achieved by arranging these compounds on a substrate and exploiting intermolecular Coulombic coupling. The operation of such a device relies on nonequilibrium electron transfer (ET), whereby the time-varying electric field of one molecule induces an ET event in a neighboring molecule. The magnitude of the electric fields can be quite large because of close spatial proximity, and the induced ET rate is a measure of the nonequilibrium response of the molecule. We calculate the electric-field-driven ET rate for a model mixed-valence compound. The mixed-valence molecule is regarded as a two-state electronic system coupled to a molecular vibrational mode, which is, in turn, coupled to a thermal environment. Both the electronic and vibrational degrees-of-freedom are treated quantum mechanically, and the dissipative vibrational-bath interaction is modeled with the Lindblad equation. This approach captures both tunneling and nonadiabatic dynamics. Relationships between microscopic molecular properties and the driven ET rate are explored for two time-dependent applied fields: an abruptly switched field and a linearly ramped field. In both cases, the driven ET rate is only weakly temperature dependent. When the model is applied using parameters appropriate to a specific mixed-valence molecule, diferrocenylacetylene, terahertz-range ET transfer rates are predicted.

Synthesis of a Neutral Mixed-Valence Diferrocenyl Carborane for Molecular Quantum-Dot Cellular Automata Applications.

The preparation of 7-Fc(+) -8-Fc-7,8-nido-[C2 B9 H10 ](-) (Fc(+) FcC2 B9 (-) ) demonstrates the successful incorporation of a carborane cage as an internal counteranion bridging between ferrocene and ferrocenium units. This neutral mixed-valence Fe(II) /Fe(III) complex overcomes the proximal electronic bias imposed by external counterions, a practical limitation in the use of molecular switches. A combination of UV/Vis-NIR spectroscopic and TD-DFT computational studies indicate that electron transfer within Fc(+) FcC2 B9 (-) is achieved through a bridge-mediated mechanism. This electronic framework therefore provides the possibility of an all-neutral null state, a key requirement for the implementation of quantum-dot cellular automata (QCA) molecular computing. The adhesion, ordering, and characterization of Fc(+) FcC2 B9 (-) on Au(111) has been observed by scanning tunneling microscopy.

Hydrogen-bonded clusters of 1, 1'-ferrocenedicarboxylic acid on Au(111) are initially formed in solution.

Low-temperature scanning tunneling microscopy is used to observe self-assembled structures of ferrocenedicarboxylic acid (Fc(COOH)2) on the Au(111) surface. The surface is prepared by pulse-deposition of Fc(COOH)2 dissolved in methanol, and the solvent is evaporated before imaging. While the rows of hydrogen-bonded dimers that are common for carboxylic acid species are observed, the majority of adsorbed Fc(COOH)2 is instead found in six-molecule clusters with a well-defined and chiral geometry. The coverage and distribution of these clusters are consistent with a random sequential adsorption model, showing that solution-phase species are determinative of adsorbate distribution for this system under these reaction conditions.

Hydrogen-bonded clusters of ferrocenecarboxylic acid on Au(111).

Self-assembled monolayers of ferrocenecarboxylic acid (FcCOOH) contain two fundamental units, both stabilized by intermolecular hydrogen bonding: dimers and cyclic five-membered catemers. At surface coverages below a full monolayer, however, there is a significantly more varied structure that includes double-row clusters containing two to twelve FcCOOH molecules. Statistical analysis shows a distribution of cluster sizes that is sharply peaked compared to a binomial distribution. This rules out simple nucleation-and-growth mechanisms of cluster formation, and strongly suggests that clusters are formed in solution and collapse into rows when deposited on the Au(111) surface.

Self-assembly of hydrogen-bonded two-dimensional quasicrystals.

The process of molecular self-assembly on solid surfaces is essentially one of crystallization in two dimensions, and the structures that result depend on the interplay between intermolecular forces and the interaction between adsorbates and the underlying substrate. Because a single hydrogen bond typically has an energy between 15 and 35 kilojoules per mole, hydrogen bonding can be a strong driver of molecular assembly; this is apparent from the dominant role of hydrogen bonding in nucleic-acid base pairing, as well as in the secondary structure of proteins. Carboxylic acid functional groups, which provide two hydrogen bonds, are particularly promising and reliable in creating and maintaining surface order, and self-assembled monolayers of benzoic acids produce structure that depends on the number and relative placement of carboxylic acid groups. Here we use scanning tunnelling microscopy to study self-assembled monolayers of ferrocenecarboxylic acid (FcCOOH), and find that, rather than producing dimeric or linear structures typical of carboxylic acids, FcCOOH forms highly unusual cyclic hydrogen-bonded pentamers, which combine with simultaneously formed FcCOOH dimers to form two-dimensional quasicrystallites that exhibit local five-fold symmetry and maintain translational and rotational order (without periodicity) for distances of more than 400 ångströms.

Adsorption of diferrocenylacetylene on Au(111) studied by scanning tunneling microscopy.

Scanning tunneling microscopy images of diferrocenylacetylene (DFA) coadsorbed with benzene on Au(111) show individual and close-packed DFA molecules, either adsorbed alongside benzene or on top of a benzene monolayer. Images acquired over a range of positive and negative tip-sample bias voltages show a shift in contrast, with the acetylene linker appearing brighter than the ferrocenes at positive sample bias (where unoccupied states primarily contribute) and the reverse contrast at negative bias. Density functional theory was used to calculate the electronic structure of the gas-phase DFA molecule, and simulated images produced through two-dimensional projections of these calculations approximate the experimental images. The symmetry of both experimental and calculated molecular features for DFA rules out a cis adsorption geometry, and comparison of experiment to simulation indicates torsion around the inter-ferrocene axis between 90° and 180° (trans); the cyclopentadienyl rings are thus angled with respect to the surface.

Through-bond versus through-space coupling in mixed-valence molecules: observation of electron localization at the single-molecule scale.

Scanning tunneling microscopy (STM) is used to study two dinuclear organometallic molecules, meta-Fe2 and para-Fe2, which have identical molecular formulas but differ in the geometry in which the metal centers are linked through a central phenyl ring. Both molecules show symmetric electron density when imaged with STM under ultrahigh-vacuum conditions at 77 K. Chemical oxidation of these molecules results in mixed-valence species, and STM images of mixed-valence meta-Fe2 show pronounced asymmetry in electronic state density, despite the structural symmetry of the molecule. In contrast, images of mixed-valence para-Fe2 show that the electronic state density remains symmetric. Images are compared to constrained density functional (CDFT) calculations and are consistent with full localization of charge for meta-Fe2 on to a single metal center, as compared with charge delocalization over both metal centers for para-Fe2. The conclusion is that electronic coupling between the two metal centers occurs through the bonds of the organic linker, and through-space coupling is less important. In addition, the observation that mixed-valence para-Fe2 is delocalized shows that electron localization in meta-Fe2 is not determined by interactions with the Au(111) substrate or the position of neighboring solvent molecules or counterion species.

Charge localization in isolated mixed-valence complexes: an STM and theoretical study.

{Cp*(dppe)Fe(C≡C-)}(2)(1,3-C(6)H(4)) is studied both as a neutral molecule, Fe(II)-Fe(II), and as a mixed-valence complex, Fe(II)-Fe(III). Scanning tunneling microscopy (STM) is used to image these species at 77 K under ultrahigh-vacuum conditions. The neutral molecule Fe(II)-Fe(II) has a symmetric, "dumbbell" appearance in STM images, while the mixed-valence complex Fe(II)-Fe(III) demonstrates an asymmetric, bright-dim double-dot structure. This asymmetry results from localization of the electron to one of the iron-ligand centers, a result which is confirmed through comparison to theoretical STM images calculated using constrained density-functional theory (CDFT). The observation of charge localization in mixed-valence complexes outside of the solution environment opens up new avenues for the control and patterning of charge on surfaces, with potential applications in smart materials and molecular electronic devices.

A metric for characterizing the bistability of molecular quantum-dot cellular automata.

Much of molecular electronics involves trying to use molecules as (a) wires, (b) diodes or (c) field-effect transistors. In each case the criterion for determining good performance is well known: for wires it is conductance, for diodes it is conductance asymmetry, while for transistors it is high transconductance. Candidate molecules can be screened in terms of these criteria by calculating molecular conductivity in forward and reverse directions, and in the presence of a gating field. Hence so much theoretical work has focused on understanding molecular conductance. In contrast a molecule used as a quantum-dot cellular automata (QCA) cell conducts no current at all. The keys to QCA functionality are (a) charge localization, (b) bistable charge switching within the cell and (c) electric field coupling between one molecular cell and its neighbor. The combination of these effects can be examined using the cell-cell response function which relates the polarization of one cell to the induced polarization of a neighboring cell. The response function can be obtained by calculating the molecular electronic structure with ab initio quantum chemistry techniques. We present an analysis of molecular QCA performance that can be applied to any candidate molecule. From the full quantum chemistry, all-electron ab initio calculations we extract parameters for a reduced-state model which reproduces the cell-cell response function very well. Techniques from electron transfer theory are used to derive analytical models of the response function and can be employed on molecules too large for full ab initio treatment. A metric is derived which characterizes molecular QCA performance the way transconductance characterizes transistor performance. This metric can be assessed from absorption measurements of the electron transfer band or quantum chemistry calculations of appropriate sophistication.

Bennett clocking of quantum-dot cellular automata and the limits to binary logic scaling.

We examine power dissipation in different clocking schemes for molecular quantum-dot cellular automata (QCA) circuits. 'Landauer clocking' involves the adiabatic transition of a molecular cell from the null state to an active state carrying data. Cell layout creates devices which allow data in cells to interact and thereby perform useful computation. We perform direct solutions of the equation of motion for the system in contact with the thermal environment and see that Landauer's Principle applies: one must dissipate an energy of at least k(B)T per bit only when the information is erased. The ideas of Bennett can be applied to keep copies of the bit information by echoing inputs to outputs, thus embedding any logically irreversible circuit in a logically reversible circuit, at the cost of added circuit complexity. A promising alternative which we term 'Bennett clocking' requires only altering the timing of the clocking signals so that bit information is simply held in place by the clock until a computational block is complete, then erased in the reverse order of computation. This approach results in ultralow power dissipation without additional circuit complexity. These results offer a concrete example in which to consider recent claims regarding the fundamental limits of binary logic scaling.

Molecular quantum cellular automata cells. Electric field driven switching of a silicon surface bound array of vertically oriented two-dot molecular quantum cellular automata.

The amine functionality of the linker on the dinuclear complex [trans-Ru(dppm)(2)(Ctbd1;CFc)(NCCH(2)CH(2)NH(2))][PF(6)] reacts with Si-Cl bonds of a chlorinated, highly B doped Si (111) surface to yield Si-N surface-complex bonds. The surface bound complex is constrained to a near vertical orientation by the chain length of the linker as confirmed by variable angle XPS. Oxidation of the dinuclear complex with ferrocenium ion or electrochemically generates a stable, biased Fe(III)-Ru(II) mixed-valence complex on the surface. Characterization of the array of surface bound complexes with spectroscopic as well as electrochemical techniques confirms the presence of strongly bound, chemically robust, mixed-valence complexes. Capping the flat array of complexes with a minimally perturbing mercury electrode permits the equalization of the Fe and Ru energy wells by an applied electric field. The differential capacitance of oxidized and unoxidized bound complexes is compared as a function of voltage applied between the Hg gate and the Si. The results show that electron exchange between the Fe and Ru sites of the array of dinuclear mixed-valence complexes at energy equalization generates a fluctuating dipole that produces a maximum in the capacitance versus voltage curve for each complex-counterion combination present. Passage through the capacitance maximum corresponds to switching of the molecular quantum cellular automata (QCA) cell array by the electric field from the Fe(III)-Ru(II) configuration to the Fe(II)-Ru(III) configuration, thereby confirming that molecules possess an essential property necessary for their use as elements of a QCA device.

Molecular quantum-dot cellular automata.

Molecular electronics is commonly conceived as reproducing diode or transistor action at the molecular level. The quantum-dot cellular automata (QCA) approach offers an attractive alternative in which binary information is encoded in the configuration of charge among redox-active molecular sites. The Coulomb interaction between neighboring molecules provides device-device coupling. No current flow between molecules is required. We present an ab initio analysis of a simple molecular system which acts as a molecular QCA cell. The intrinsic bistability of the charge configuration results in dipole or quadrupole fields which couple strongly to the state of neighboring molecules. We show how logic gates can be implemented. We examine the role of the relaxation of nuclear coordinates in the molecular charge reconfiguration.

A two-stage shift register for clocked Quantum-Dot Cellular Automata.

Quantum-Dot Cellular Automata (QCA) is a computational scheme utilizing the position of interacting single electrons within arrays of quantum dots ("cells") to encode and process binary information. Clocked QCA architectures can provide power gain, logic level restoration, and memory features. Using arrays of micron-sized metal dots, we experimentally demonstrate operation of a QCA latch-inverter and a two-stage shift register.