Engineered Quantum Systems Research Articles

Compressed sensing for Hamiltonian reconstruction

In engineered quantum systems, the Hamiltonian is often not completely known and needs to be determined experimentally with accuracy and efficiency. We show that this may be done at temperatures that are greater than the characteristic interaction energies, but not too much greater. The condition for this is that there are not too many interactions: the Hamiltonian is sparse in a well-defined sense. The protocol that accomplishes this is related to compressed sensing methods of classical signal processing; in this case applied to sparse rather than low-rank matrices.

Vibrationally assisted quantum energy pumps

We show that directed energy transport in a linear array of coupled quantum dots can be achieved by a coherent coupling of each dot to a single coherently driven mechanical mode. Recent work on light harvesting molecules have implicated the role of discrete mechanical modes in enhancing the energy transport through dipole arrays but say less about directed transport. The study of quantum ratchets indicates how directed energy transport is possible in quantum dot arrays. Inspired by these two apparently unrelated models we show how directed energy transport may be implemented in an engineered quantum systems using a single mechanical degree of freedom. This may have implications for nano-engineered artificial energy harvesting systems.

Heisenberg picture approach to the stability of quantum Markov systems

Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, which extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks.

Ultrasensitive microwave spectroscopy of paramagnetic impurities in sapphire crystals at millikelvin temperatures

Progress in the emerging field of engineered quantum systems requires the development of devices that can act as quantum memories. The realization of such devices by doping solid-state cavities with paramagnetic ions imposes a tradeoff between ion concentration and cavity coherence time. Here, we investigate an alternative approach involving interactions between photons and naturally occurring impurity ions in ultrapure crystalline microwave cavities exhibiting exceptionally high quality factors. We implement a hybrid whispering gallery/electron spin resonance method to perform rigorous spectroscopy of an undoped single-crystal sapphire resonator over the frequency range 8--19 GHz, and at external applied DC magnetic fields up to 0.9 T. Measurements of high-purity sapphire cooled close to 100 mK reveal the presence of Fe${}^{3+}$, Cr${}^{3+}$, and V${}^{2+}$ impurities. A host of electron transitions are measured and identified, including the two-photon classically forbidden quadrupole transition ($\ensuremath{\Delta}{m}_{s}=2$) for Fe${}^{3+}$, as well as hyperfine transitions of V${}^{2+}$.

Entangling Mechanical Motion with Microwave Fields

When two physical systems share the quantum property of entanglement, measurements of one system appear to determine the state of the other. This peculiar property is used in optical, atomic, and electrical systems in an effort to exceed classical bounds when processing information. We extended the domain of this quantum resource by entangling the motion of a macroscopic mechanical oscillator with a propagating electrical signal and by storing one half of the entangled state in the mechanical oscillator. This result demonstrates an essential requirement for using compact and low-loss micromechanical oscillators in a quantum processor, can be extended to sense forces beyond the standard quantum limit, and may enable tests of quantum theory.

A Single-Atom Lasso

Physics Optical tweezing is a powerful technique for trapping and manipulating particles and can be applied to a broad range of size scales—from single cells and viruses to glass beads several micrometers in diameter. Tweezing can also be used to trap single atoms. However, the interaction between photons in the trapping light beam and the atom generally results in atom jitter. This motion of the atom tends to prevent the atoms from being cooled to the lowest temperatures, where interesting quantum effects can then be probed. Kaufman et al. used an optical trapping beam and a suite of laser pulses to lasso a single rubidium atom and exploited Raman transitions of the atom to cool it to the quantum ground state. Once trapped and cooled to remove all vibrations from the atom, they also show that they could coherently manipulate its quantum spin and motion. The generality and flexibility of the optical tweezing approach may allow more complex systems comprising arrays of overlapping and interacting trapped atoms or molecules to be designed to form quantum simulators (i.e., well-controlled, engineered quantum systems that can be used to model other less-well-understood condensed-matter systems). Phys. Rev. X 2 , 041014 (2012).

Observation of topologically protected bound states in photonic quantum walks

Topological phases exhibit some of the most striking phenomena in modern physics. Much of the rich behaviour of quantum Hall systems, topological insulators, and topological superconductors can be traced to the existence of robust bound states at interfaces between different topological phases. This robustness has applications in metrology and holds promise for future uses in quantum computing. Engineered quantum systems--notably in photonics, where wavefunctions can be observed directly--provide versatile platforms for creating and probing a variety of topological phases. Here we use photonic quantum walks to observe bound states between systems with different bulk topological properties and demonstrate their robustness to perturbations--a signature of topological protection. Although such bound states are usually discussed for static (time-independent) systems, here we demonstrate their existence in an explicitly time-dependent situation. Moreover, we discover a new phenomenon: a topologically protected pair of bound states unique to periodically driven systems.

Optimal control of the electronic current density: Application to one- and two-dimensional one-electron systems

Quantum optimal control theory is a powerful tool for engineering quantum systems subject to external fields such as the ones created by intense lasers. The formulation relies on a suitable definition for a target functional, that translates the intended physical objective to a mathematical form. We propose the use of target functionals defined in terms of the one-particle density and its current. A strong motivation for this is the possibility of using time-dependent density-functional theory for the description of the system dynamics. We exemplify this idea by defining an objective functional that on one hand attempts a large overlap with a target density and on the other hand minimizes the current. The latter requirement leads to optimized states with increased stability, which we prove with a few examples of one- and two-dimensional one-electron systems.

Adaptive quantum design of atomic clusters

Adaptive quantum design identifies the best broken-symmetry configurations of atoms and molecules that enable a desired target function response. In this work, numerical optimization is used to design atomic clusters with specified quasiparticle densities of states. The dominant self-assembled building blocks of these engineered quantum systems are found to depend on the symmetry of the target function. For example, particle-hole symmetric spectra can be constructed from a dilute configuration of atomic dimers, whereas more complex structures such as trimers and quadrumers are required for asymmetric target functions. The convergence of the optimization algorithms depends on the shape of the target function, the density of atoms, and constraints due to substrates and boundary conditions. Hybrids of steepest descent methods, simulated annealing, and genetic algorithms are found to be most efficient.