We propose a method for a weak continuous measurement of the energy eigenstates of a fast quantum system by means of a slow detector. Such a detector is sensitive only to slowly changing variables, e.g., energy, while its backaction can be limited solely to decoherence of the eigenstate superpositions. We apply this scheme to the problem of detection of quantum jumps between energy eigenstates in a harmonic oscillator.

The quantum dynamics of colliding Bose-Einstein condensates with 150 000 atoms are simulated directly from the Hamiltonian using the stochastic positive-$P$ method. Two-body correlations between the scattered atoms and their velocity distribution are found for experimentally accessible parameters. Hanbury Brown–Twiss or thermal-like correlations are seen for copropagating atoms, while number correlations for counterpropagating atoms are even stronger than thermal correlations at short times. The coherent phase grains grow in size as the collision progresses with the onset of growth coinciding with the beginning of stimulated scattering. The method is versatile and usable for a range of cold atom systems.

We report on measurements of resonantly enhanced tunneling of Bose-Einstein condensates loaded into an optical lattice. By controlling the initial conditions of our system we were able to observe resonant tunneling in the ground and the first two excited states of the lattice wells. We also investigated the effect of the intrinsic nonlinearity of the condensate on the tunneling resonances.

We map adiabatic quantum evolution on the classical Hamiltonian dynamics of a 1D gas (Pechukas gas) and simulate the latter numerically. This approach turns out to be both insightful and numerically efficient, as seen from our example of a CNOT gate simulation. For a general class of Hamiltonians we show that the escape probability from the initial state scales no faster than $|\dot{\lambda }{|}^{\gamma }$, where $|\dot{\lambda }|$ is the adiabaticity parameter. The scaling exponent for the escape probability is $\gamma =\frac{1}{2}$ for all levels, except the edge (bottom and top) ones, where $\gamma \lesssim \frac{1}{3}$. In principle, our method can solve arbitrarily large adiabatic quantum Hamiltonians.

We show that nonlinear resonances in a classically mixed phase space allow us to define generic, strongly entangled multipartite quantum states. The robustness of their multipartite entanglement increases with the particle number, i.e., in the semiclassical limit, for those classes of diffusive noise which assist the quantum-classical transition.

We factor the number 157573 using an NMR implementation of Gauss sums. Although the current implementation is classical and scales exponentially, we believe that an extension to the quantum regime using entangled states is possible.

We develop cluster algorithms for a broad class of loop models on two-dimensional lattices, including several standard $O(n)$ loop models at $n\ge 1$. We show that our algorithm has little or no critical slowing-down when $1\le n\le 2$. We use this algorithm to investigate the honeycomb-lattice $O(n)$ loop model, for which we determine several new critical exponents, and a square-lattice $O(n)$ loop model, for which we obtain new information on the phase diagram.

We propose quantum-cryptographic protocols to secretly communicate a reference frame—unspeakable information in the sense it cannot be encoded into a string of bits. Two distant parties can secretly align their Cartesian axes by exchanging $N$ spin-$\frac{1}{2}$ particles, achieving the optimal accuracy $1/N$. A possible eavesdropper cannot gain any information without being detected.

We present a method to estimate entanglement measures in experiments. We show how a lower bound on a generic entanglement measure can be derived from the measured expectation values of any finite collection of entanglement witnesses. Hence witness measurements are given a quantitative meaning without the need of further experimental data. We apply our results to a recent multiphoton experiment [M. Bourennane et al., Phys. Rev. Lett. 92, 087902 (2004)], giving bounds on the entanglement of formation and the geometric measure of entanglement in this experiment.

We study the computational complexity of the $N$-representability problem in quantum chemistry. We show that this problem is quantum Merlin-Arthur complete, which is the quantum generalization of nondeterministic polynomial time complete. Our proof uses a simple mapping from spin systems to fermionic systems, as well as a convex optimization technique that reduces the problem of finding ground states to $N$ representability.

We analyze the quantum phase transition in the Bose-Hubbard model borrowing two tools from quantum-information theory, i.e., the ground-state fidelity and entanglement measures. We consider systems at unitary filling comprising up to 50 sites and show for the first time that a finite-size scaling analysis of these quantities provides excellent estimates for the quantum critical point. We conclude that fidelity is particularly suited for revealing a quantum phase transition and pinning down the critical point thereof, while the success of entanglement measures depends on the mechanisms governing the transition.

We present a simple, robust, and highly efficient method for optimizing all parameters of many-body wave functions in quantum Monte Carlo calculations, applicable to continuum systems and lattice models. Based on a strong zero-variance principle, diagonalization of the Hamiltonian matrix in the space spanned by the wave function and its derivatives determines the optimal parameters. It systematically reduces the fixed-node error, as demonstrated by the calculation of the binding energy of the small but challenging ${\mathrm{C}}_2$ molecule to the experimental accuracy of 0.02 eV.

Dilute gas Bose-Einstein condensates (BEC’s), currently used to cool fermionic atoms in atom traps, can also probe the superfluidity of these fermions. The damping rate of BEC-acoustic excitations (phonon modes), measured in the middle of the trap as a function of the phonon momentum, yields an unambiguous signature of BCS-like superfluidity, provides a measurement of the superfluid gap parameter, and gives an estimate of the size of the Cooper pairs in the BEC-BCS crossover regime. We also predict kinks in the momentum dependence of the damping rate which can reveal detailed information about the fermion quasiparticle dispersion relation.

We propose scalable architectures for the coherence-preserving qubits introduced by Bacon, Brown, and Whaley [Phys. Rev. Lett. 87, 247902 (2001)]. These architectures employ extra qubits providing additional degrees of freedom to the system. These extra degrees of freedom can be used to counter coupling strength errors within the coherence-preserving qubit and combat interactions with environmental qubits. Importantly, these architectures provide flexibility in qubit arrangement, allowing all physical qubits to be arranged in two spatial dimensions.

The density of two initially independent condensates which are allowed to expand and overlap can show interferences as a function of time due to interparticle interaction. Two situations are separately discussed and compared: (1) all atoms are identical and (2) each condensate consists of a different kind of atoms. Illustrative examples are presented.

Weak dipolar effects in atomic Bose-Einstein condensates (BECs) have recently been predicted to develop spin textures. However, observation of the spin textures requires us to decrease the magnetic field down to $\sim 10\mu \mathrm{G}$ for spin-1 alkali BECs, so that they are not washed out by the Zeeman effect. We present a scheme to observe the magnetic dipole-dipole interaction in alkali BECs under a realistic magnetic field of $\sim 100\mathrm{mG}$. Our scheme enables us to extract genuine dipolar effects and should apply also to ${}^{52}\mathrm{Cr}$ BECs.

We present phase diagrams for population-imbalanced, trapped Fermi superfluids near unitarity. In addition to providing quantitative values for the superfluid transition temperature, the pairing onset temperature, and the transition line (separating the Sarma and phase separation regimes), we study experimental signatures of these transitions based on density profiles and density differences at the center. Predictions on the BCS side of resonance show unexpected behavior, which should be searched for experimentally.

We present coherence-enhanced imaging, an in situ technique that uses Raman superradiance to probe the spatial coherence of an ultracold gas. Applying this technique, we identify the coherent portion of an inhomogeneous degenerate ${}^{87}\mathrm{Rb}$ gas and obtain a spatially resolved measurement of the first-order spatial correlation function. We find that the decay of spin gratings is enhanced in high density regions of a Bose-Einstein condensate, and ascribe the enhancement to collective atom-atom scattering. Further, we directly observe spatial inhomogeneities that arise generally in the course of extended-sample superradiance.

We report observations of vortex formation by merging and interfering multiple ${}^{87}\mathrm{Rb}$ Bose-Einstein condensates (BECs) in a confining potential. In this experiment, a single harmonic potential well is partitioned into three sections by a barrier, enabling the simultaneous formation of three independent, uncorrelated BECs. The BECs may either automatically merge together during their growth, or for high-energy barriers, the BECs can be merged together by barrier removal after their formation. Either process may instigate vortex formation in the resulting BEC, depending on the initially indeterminate relative phases of the condensates and the merging rate.

The ergodic hypothesis is viewed as one that is physically measurable through scattering by an external probe. Linear response theory is used to derive a general ergodic condition on the response functions. It is shown that the same condition is also implied by Birkhoff’s theorem. This coincidence allows us to shed light on the abstract terms of the theorem via classical many-body models.