No abstract

We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat nonlinearities efficiently and by introducing tensor networks as a programming paradigm. The key concepts of the algorithm are demonstrated for the nonlinear Schrödinger equation as a canonical example. We numerically show that the variational quantum ansatz can be exponentially more efficient than matrix product states and present experimental proof-of-principle results obtained on an IBM Q device. arXiv:1907.09032v2 [quant-ph]

A two-mode single-atom laser is considered, with the aim of generating entanglement in macroscopic light. Two transitions in the four-level gain medium atom independently interact with the two cavity modes, while two other transitions are driven by control laser fields. Atomic relaxation as well as cavity losses are taken into account. We show that this system is a source of macroscopic entangled light over a wide range of control parameters and initial states of the cavity field

We propose a scheme for preparing nanomechanical oscillators in nonclassical steady states, characterized by a pronounced negative Wigner function. In our optomechanical approach, the mechanical oscillator couples to multiple laser-driven resonances of an optical cavity. By lowering the resonance frequency of the oscillator via an inhomogeneous electrostatic field, we significantly enhance its intrinsic geometric nonlinearity per phonon. This causes the motional sidebands to split into separate spectral lines for each phonon number and transitions between individual phonon Fock states can be selectively addressed. We show that this enables the preparation of the nanomechanical oscillator in a single-phonon Fock state. Our scheme can, for example, be implemented with a carbon nanotube dispersively coupled to the evanescent field of a state of the art whispering gallery mode microcavity.

We show that the dipole-dipole interaction between two Rydberg atoms can give rise to long range molecules. The binding potential arises from two states that converge to different separated atom asymptotes. These states interact weakly at large distances, but start to repel each other strongly as the van der Waals interaction turns into a resonant dipole-dipole interaction with decreasing separation between the atoms. This mechanism leads to the formation of an attractive well for one of the potentials. If the two separated atom asymptotes come from the small Stark splitting of an atomic Rydberg level, which lifts the Zeeman degeneracy, the depth of the well and the location of its minimum are controlled by the external electric field. We discuss two different geometries that result in a localized and a donut shaped potential, respectively.

We present an experimental demonstration of converting a microwave field to an optical field via frequency mixing in a cloud of cold ^{87}Rb atoms, where the microwave field strongly couples to an electric dipole transition between Rydberg states. We show that the conversion allows the phase information of the microwave field to be coherently transferred to the optical field. With the current energy level scheme and experimental geometry, we achieve a photon-conversion efficiency of ∼0.3% at low microwave intensities and a broad conversion bandwidth of more than 4 MHz. Theoretical simulations agree well with the experimental data, and they indicate that near-unit efficiency is possible in future experiments.

We show that the dipole-dipole interaction between three identical Rydberg atoms can give rise to bound trimer states. The microscopic origin of these states is fundamentally different from Efimov physics. Two stable trimer configurations exist where the atoms form the vertices of an equilateral triangle in a plane perpendicular to a static electric field. The triangle edge length typically exceeds R ≈ 2 µm, and each configuration is two-fold degenerate due to Kramers' degeneracy. The depth of the potential wells and the triangle edge length can be controlled by external parameters. We establish the Borromean nature of the trimer states, analyze the quantum dynamics in the potential wells and describe methods for their production and detection. PACS numbers: 34.20Cf,32.80.Ee,82.20.Rp Rydberg atoms [1] are ideal candidates for the investigation of few-body quantum phenomena for several reasons. First, their internal and external degrees of freedom can be accurately controlled and manipulated in stateof-the-art experiments. This gives rise to theoretically well-understood and tunable dipole-dipole (DD) interactions [2, 3] between ultra-cold Rydberg atoms. Second, the range of these DD interactions is extremely large -it typically extends to several microns. This feature allows the study of few-body quantum systems whose constituents can be prepared, manipulated and detected individually. Several quantum phenomena arising from strong interactions between two Rydberg atoms were investigated recently. Examples are given by the Rydberg blockade effect [4][5][6][7] and the realization of quantum gates and entanglement [8,9]. Rydberg atoms can form giant diatomic molecules via different binding mechanisms between their constituents [10][11][12][13][14][15]. Artificial gauge fields induced by the DD interaction [16,17] and acting on the relative motion of two Rydberg atoms were predicted in [18][19][20].In few body-physics, systems with three particles often show qualitatively different features as compared to two particles [21][22][23][24][25][26][27][28][29][30][31]. For example, it has been shown [21] that the dipole blockade can be broken by adding a third Rydberg atom. Furthermore, it has been predicted [22] that systems of more than two DD interacting atoms exhibit conical intersections [23,24], which are relevant for photo-chemical processes. A paradigm of few-body quantum physics is the Efimov effect [25][26][27][28]. Here a short-range resonant two-body interaction between identical bosons gives rise to a universal set of bound trimer states [29]. Recently, it was shown that the Efimov effect persists [30] even for a resonant long-range DD interaction.Here we show that the DD interaction between three distant Rydberg atoms with non-overlapping electron clouds can induce bound trimer states. These states arise from the rich internal level structure of the Rydberg atoms. A crucial point is the presence of several dipole transitions in each atom and the interplay between distance-dependent DD interactions and ...

The interplay of the concepts of complementarity and interference in the time-energy domain are studied. In particular, we theoretically investigate the fluorescence light from a J = 1/2 to J= 1/2 transition that is driven by a monochromatic laser field. We find that the spectrum of resonance fluorescence exhibits a signature of vacuum-mediated interference effects, whereas the total intensity is not affected by interference. We demonstrate that this result is a consequence of the principle of complementarity, applied to time and energy. Since the considered level scheme can be found, e.g., in (198)Hg(+) ions, our model system turns out to be an ideal candidate to provide evidence for as yet experimentally unconfirmed vacuum-induced atomic coherences.