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A collective spin model is used to describe two species of mutually interacting ultracold bosonic atoms confined to a toroidal trap. The system is modeled by a Hamiltonian that can be split into two components, a linear part and a quadratic part, which may be controlled independently. We show the linear component is an analog of a Zeeman Hamiltonian, and the quadratic component presents a macroscopic simulator for spin-orbit and hyperfine interactions. We determine a complete set of commuting observables for both the linear and quadratic Hamiltonians, and derive analytical expressions for their respective spectra and density of states. We determine the conditions for generating maximal entanglement between the two species of atoms with a view to applications involving quantum correlations among spin degrees of freedom, such as in the area of quantum information., Comment: 9 pages; 5 figures

We put forth the concept of quantum noise sensing in nonlinear two-mode interferometers coupled to mechanical oscillators. These autonomous machines are capable of sensing quantum nonlinear correlations of two-mode noisy fields via their thermodynamic variable of extractable work, alias work capacity or ergotropy. The fields are formed by thermal noise input via its interaction with multi-level systems inside the interferometer. Such interactions amount to the generation of two-mode quantum nonlinear gauge fields that may be partly unknown. We show that by monitoring a mechanical oscillator coupled to the interferometer, one can sense the work capacity of one of the output field modes and thereby reveal the quantum nonlinear correlations of the field. The proposed quantum sensing method can provide an alternative to quantum multiport interferometry where the output field is unraveled by tomography. This method may advance the simulation and control of multimode quantum nonlinear gauge fields., Comment: To be published in Quantum Science and Technology

Estimation of the phase delay between interferometer arms is the core of transmission phase microscopy. Such phase estimation may exhibit an error below the standard quantum (shot-noise) limit, if the input is an entangled two-mode state, e.g., a N00N state. We show, by contrast, that such supersensitive phase estimation (SSPE) is achievable by \textit{incoherent}, e.g., \textit{thermal}, light that is injected into a Mach-Zehnder interferometer via a Kerr-nonlinear two-mode coupler. Phase error is shown to be reduced below $1/\bar{n}$, $\bar{n}$ being the mean photon number, by thermal input in such interferometric setups, even for small nonlinear phase-shifts per photon pair or for significant photon loss. Remarkably, the phase accuracy achievable in such setups by thermal input surpasses that of coherent light with the same $\bar{n}$. Available mode couplers with giant Kerr nonlinearity that stems either from dipole-dipole interactions of Rydberg polaritons in a cold atomic gas, or from cavity-enhanced dispersive atom-field interactions, may exploit such effects to substantially advance interferometric phase microscopy using incoherent, faint light sources., Comment: Accepted for publication in Phys. Rev. A

We study the general quantum Hamiltonian that can be realized with two species of mutually interacting degenerate ultracold atoms in a ring-shaped trap, with the options of rotation and an azimuthal lattice. We examine the spectrum and the states with a collective spin picture in a Dicke state basis. The system can generate states with a high degree of entanglement gauged by the von Neumann entropy. The Hamiltonian has two components, a linear part that can be controlled and switched on via rotation or the azimuthal lattice, and an interaction-dependent quadratic part. Exact solutions are found for the quadratic part for equal strengths of intra-species and the inter-species interactions, but for generally different particle numbers in the two species. The quadratic Hamiltonian has a degenerate ground state when the two species have unequal number of particles, but non-degenerate when equal. We determine the impact on the entanglement entropy of deviations from equal particle numbers as well as deviations from the assumption of equal interaction strengths. Limiting cases are shown to display features of a beam-splitter and spin-squeezing that can find utility in interferometry. The density of states for the full Hamiltonian shows features as of phase transition in varying between linear and quadratic limits., Comment: 8 pages, 6 figures

Our goal in this article is to elucidate the rapport of work and information in the context of a minimal quantum mechanical setup: A converter of heat input to work output, the input consisting of a single oscillator mode prepared in a hot thermal state along with few much colder oscillator modes. We wish to achieve heat to work conversion in the setup while avoiding the use of a working substance (medium) or macroscopic heat baths. The core issues we consider, taking account of the quantum nature of the setup, are: (i) How and to what extent can information act as work resource or, conversely, be redundant for work extraction? (ii) What is the optimal way of extracting work via information acquired by measurements? (iii) What is the bearing of information on the efficiency-power tradeoff achievable in such setups? We compare the efficiency of work extraction and the limitations of power in our minimal setup by unitary (reversible) manipulations and by different, generic, measurement strategies of the hot and cold modes. For each strategy the rapport of work and information extraction is found and the cost of information erasure is allowed for. The possibilities of work extraction without information acquisition, via non-selective measurements, are also analyzed. Overall, we present, by generalizing a method based on optimized homodyning that we have recently proposed, the following insight: extraction of work by observation and feedforward (WOF) that only measures a small fraction of the input, is clearly advantageous to the conceivable alternatives. Our results may become a basis of a practical strategy of converting thermal noise to useful work in optical setups, such as coherent amplifiers of thermal light, as well as in their optomechanical and photovoltaic counterparts., Comment: 30 pages including appendix of 6 pages

All existing heat machines are dissipative open systems. Hence, they cannot operate fully coherently. We propose to replace this conventional thermodynamic paradigm by a completely different one, whereby heat machines are nonlinear coherent closed systems comprised of few field modes. Their thermal-state input is transformed by nonlinear interactions into non-thermal output with controlled quantum fluctuations and the capacity to deliver work in a chosen mode. This new paradigm allows the bridging of quantum coherent and thermodynamic descriptions., Comment: 10 pages, 4 figures. Updated version, modified title and extended number of authors

We put forward the concept of work extraction from thermal noise by phase-sensitive (homodyne) measurements of the noisy input followed by (outcome-dependent) unitary manipulations of the post-measured state. For optimized measurements, noise input with more than one quantum on average is shown to yield heat-to-work conversion with efficiency and power that grow with the mean number of input quanta, detector efficiency and its inverse temperature. This protocol is shown to be advantageous compared to common models of information and heat engines., Comment: 6+18 pages, Close to the accepted version in PRL

We experimentally demonstrate, for the first time, noise diagnostics by repeated quantum measurements. Specifically, we establish the ability of a single photon, subjected to random polarisation noise, to diagnose non-Markovian temporal correlations of such a noise process. In the frequency domain, these noise correlations correspond to colored noise spectra, as opposed to the ones related to Markovian, white noise. Both the noise spectrum and its corresponding temporal correlations are diagnosed by probing the photon by means of frequent, (partially-)selective polarisation measurements. Our main result is the experimental demonstration that noise with positive temporal correlations corresponds to our single photon undergoing a dynamical regime enabled by the quantum Zeno effect (QZE), while noise characterized by negative (anti-) correlations corresponds to regimes associated with the anti-Zeno effect (AZE). This demonstration opens the way to a new kind of noise spectroscopy based on QZE and AZE in photon (or other single-particle) state probing.

We put forward a quantum-optical model for a thermal diode based on heat transfer between two thermal baths through a pair of interacting qubits. We find that if the qubits are coupled by a Raman field that induces an anisotropic interaction, heat flow can become non-reciprocal and undergoes rectification even if the baths have equal dissipation rates and/or the qubits are resonant. The heat flow rectification is explained by four-wave mixing and Raman transitions between dressed states of the interacting qubits and are governed by a global master equation. The anisotropic two-qubit interaction is the key for this present simple quantum thermal diode, whose resonant operation allows for high-efficiency rectification of large heat currents. Effects of spatial overlap of the baths are addressed. We also discuss the possible realizations of the model system in various platforms including optomechanical systems, systems of trapped ions, and circuit QED., Comment: Comments are welcome

We show that the classical model of Euler top (freely rotating, generally asymmetric rigid body), possibly supplemented with a rotor, corresponds to a generalized Lipkin-Meshkov-Glick (LMG) model describing phenomena of various branches of quantum physics. Classical effects such as free precession of a symmetric top, Feynman's wobbling plate, tennis-racket instability and the Dzhanibekov effect, attitude control of satellites by momentum wheels, or twisting somersault dynamics, have their counterparts in quantum effects that include spin squeezing by one-axis twisting and two-axis countertwisting, transitions between the Josephson and Rabi regimes of a Bose-Einstein condensate in a double-well potential, and other quantum critical phenomena. The parallels enable us to expand the range of explored quantum phase transitions in the generalized LMG model, as well as to present a classical analogy of the recently proposed LMG Floquet time crystal., Comment: 21 pages, 14 figures

Life is dependent on the income of energy with low entropy and the disposal of energy with high entropy. On Earth, the low-entropy energy is provided by solar radiation and the high-entropy energy is disposed as infrared radiation emitted into the cold space. Here we turn the situation around and assume cosmic background radiation as the low-entropy source of energy for a planet orbiting a black hole into which the high-entropy energy is disposed. We estimate the power that can be produced by thermodynamic processes on such a planet, with a particular interest in planets orbiting a fast rotating Kerr black hole as in the science fiction movie {\em Interstellar}. We also briefly discuss a reverse Dyson sphere absorbing cosmic background radiation from the outside and dumping waste energy to a black hole inside., Comment: 8 pages, 6 figures. Replaced with the version published in Am. J. Phys

We examine the dynamics of circulating modes of a Bose-Einstein condensate confined in toroidal lattice. Nonlinearity due to interactions leads to criticality that separates oscillatory and self-trapped phases among counter-propagating modes which however share the same physical space. In the mean-field limit, the criticality is found to substantially enhance sensitivity to rotation of the system. Analysis of the quantum dynamics reveals the fluctuations near criticality are significant, that we explain using spin-squeezing formalism visualized on a Bloch sphere. We utilize the squeezing to propose a Ramsey interferometric scheme that suppresses fluctuation in the relevant quadrature sensitive to rotation., Comment: 11 pages, 9 figures (Fig. 9 resolution reduced to meet size limits)

A method is presented to transfer a system of two-level atoms from a spin coherent state to a maximally spin squeezed Dicke state, relevant for quantum metrology and quantum information processing. The initial state is the ground state of an initial linear Hamiltonian which is gradually turned into a final quadratic Hamiltonian whose ground state is the selected Dicke state. We use compensating operators to suppress diabatic transitions to unwanted states that would occur if the change were not slow. We discuss the possibilities of constructing the compensating operators by sequential application of quadratic Hamiltonians available in experiments., Comment: 10 pages, 10 figures. Replaced with published version

A simple formula is derived for the maximum squeezing rate which occurs at the initial stages of the squeezing process: the rate only depends on the second partial derivatives of a classical Hamiltonian. Rules for optimum rotation of the phase space are found to keep the state optimally located and oriented for fastest squeezing. These operations transform the phase-space point of interest into a saddle point with opposite principal curvatures. Similar results are found for the Bloch-sphere phase space and spin squeezing. Application of the general formulas is illustrated by several model examples including parametric downconversion, Kerr nonlinearity, Jaynes-Cummings interaction, and spin squeezing by one-axis twisting and two-axis countertwisting., Comment: 14 pages, 10 figures, PRA

We propose a scheme for spin-squeezing in the orbital motion of a Bose-Einstein condensate (BEC) in a toroidal trap. A circular lattice couples two counter-rotating modes and squeezing is generated by the nonlinear interaction spatially modulated at half the lattice period. By varying the amplitude and phase of the modulation, various cases of the twisting tensor can be directly realized, leading to different squeezing regimes. These include one-axis twisting and the two-axis counter-twisting which are often discussed as the most important paradigms for spin squeezing. Our scheme naturally realizes the Lipkin-Meshkov-Glick model with the freedom to vary all its parameters simultaneously., Comment: 9 pages, 6 figures, to appear in PRA

Based on the recent twisting-tensor approach [T. Opatrny, ArXiv:1408.3265 (2014)], a specific scenario for fast and deep spin squeezing is proposed. Initially the state is subjected to one-axis twisting under optimum orientation, enabling the maximum squeezing rate allowed by the system nonlinearity. Later on, when for highly squeezed states the one-axis twisting deforms the uncertainty ellipse and deteriorates the squeezing properties, the process is switched to an effective two-axis counter-twisting by a sequence of $\pi/2$ pulses. The squeezing rate then slows to 2/3 of the maximum value, but the process can continue for longer to achieve a very high degree of squeezing., Comment: 4 pages, 4 figures

A unified tensor description of quadratic spin squeezing interactions is proposed, covering the single- and two-axis twisting as special cases of a general scheme. A closed set of equations of motion of the first moments and variances is derived in Gaussian approximation and their solutions are discussed from the prospect of fastest squeezing generation. It turns out that the optimum rate of squeezing generation is governed by the difference between the largest and the smallest eigenvalues of the twisting tensor. A cascaded optical interferometer with Kerr nonlinear media is proposed as one of possible realizations of the general scheme., Comment: 6 pages, 3 figures, to appear in PRA

The nonadiabatic dynamics of a many-body system driven through a quantum critical point can be controlled using counterdiabatic driving, where the formation of excitations is suppressed by assisting the dynamics with auxiliary multiple-body nonlocal interactions. We propose an alternative scheme which circumvents practical challenges to realize shortcuts to adiabaticity in mesoscopic systems by tailoring the functional form of the auxiliary counterdiabatic interactions. A driving scheme resorting in few-body short-range interactions is shown to generate an effectively adiabatic dynamics., Comment: Slightly improved version as published in Phys. Rev. A Rapid Communication

The quantum speed limit sets the minimum time required to transfer a quantum system completely into a given target state. At shorter times the higher operation speed has to be paid with a loss of fidelity. Here we quantify the trade-off between the fidelity and the duration in a system driven by a time-varying control. The problem is addressed in the framework of Hilbert space geometry offering an intuitive interpretation of optimal control algorithms. This approach is applied to non-uniform time variations which leads to a necessary criterion for control optimality applicable as a measure of algorithm convergence. The time fidelity trade-off expressed in terms of the direct Hilbert velocity provides a robust prediction of the quantum speed limit and allows to adapt the control optimization such that it yields a predefined fidelity. The results are verified numerically in a multilevel system with a constrained Hamiltonian, and a classification scheme for the control sequences is proposed based on their optimizability., Comment: 7 pages, 4 figures

We present a mechanism for quantum gates where the qubits are encoded in the population distribution of two component ultracold atoms trapped in a species-selective triple-well potential. The gate operation is a specific application of a new design for an atomtronics transistor where inter-species interaction is used to control transport, and can be realized with either individual atoms or aggregates like Bose-Einstein condensates (BEC). We demonstrate the operational principle with a static external potential, and show feasible implementation with a smooth dynamical potential., Comment: 5 pages,5 figures

A scheme is proposed to prepare squeezed states and Schr\"{o}dinger cat-like states of the collective spin degrees of freedom associated with a pair of ground states in an atomic ensemble. The scheme uses an effective Jaynes-Cummings interaction which can be provided by excitation of the atoms to Rydberg states and an effective J_x interaction implemented by a resonant Raman coupling between the atomic ground states. Both dynamical evolution with a constant Hamiltonian and with adiabatic variation of the two interaction terms are studied. We show that by the application of further resonant laser fields, we can suppress non-adiabatic transfer under the time varying Hamiltonian and significantly speed up the evolution towards a maximally squeezed, J_z=0, collective spin state., Comment: 11 pages, 11 figures

In an optical superlattice of triple wells, containing two mutually interacting atom species in adjacent wells, we show that one species can be transported through the positions of the other species, yet avoiding significant overlap and direct interaction. The transfer protocol is optimized to be robust against missing atoms of either species in any lattice site, as well as against lattice fluctuations. The degree and the duration of the inter-species overlap during passage can be tuned, making possible controlled large-scale interaction-induced change of internal states., Comment: 7 pages and 5 figures

A review is given on phase-sensitive measurements, such as homodyne detection, for radiation fields and material systems. Methods of quantum-state reconstruction are considered for radiation fields, including multimode and pulsed radiation. For matter systems, methods are reported for the reconstruction of quantum states of molecular vibrations, the quantized motion of trapped atoms, Bose-Einstein condensates, atomic matter waves, electron motion, spin and angular momentum systems, and crystal lattices., Comment: 119 pages, 23 figures. Volume XXXIX of Progress in Optics is out of print, while the topic of our review article continues to be of interest

Analytical expressions are derived for coherent tunneling via adiabatic passage (CTAP) in a triple well system with negligible central-well population at all times during the transfer. It is shown that a manipulation of the depths of the extreme-wells, correlated with the time variation of the \emph{non-adjacent} barriers is essential for maintaining vanishing population of the central well. The validity of our conditions are demonstrated with a numerical solution of the time-dependent Schr\"{o}dinger equation. The transfer process is interpreted in terms of a current through the central well., Comment: 7 pages; 3 figures

We show that quantum pumping does not always require a quantum description or a quantum phase. Quantum pumping is shown to encompass different types of processes, some of which intrinsically rely on phase while others do not. We also show that many pumping processes have a hidden antisymmetric component that contributes significantly to the instantaneous current at the terminals without causing net charge transfer in a period. We have also computed the exact pumped current for some cases over a full range of time variation from adiabatic to non-adiabatic., Comment: 5 pages; 3 figures

Recent experiments demonstrating atomic quantum memory for light [B. Julsgaard et al., Nature 432, 482 (2004)] involve two macroscopic samples of atoms, each with opposite spin polarization. It is shown here that a single atomic cell is enough for the memory function if the atoms are optically pumped with suitable linearly polarized light, and quadratic Zeeman shift and/or ac Stark shift are used to manipulate rotations of the quadratures. This should enhance the performance of our quantum memory devices since less resources are needed and losses of light in crossing different media boundaries are avoided., Comment: 6 pages, 2 figures, to be published in Phys. Rev. A

We predict that if internal and momentum states of an interfering object are correlated (entangled), then by measuring its internal state we may infer both path (corpuscular) and phase (wavelike) information with much higher precision than for objects lacking such entanglement. We thereby partly circumvent the standard complementarity constraints of which-path detection., Comment: 5 pages, 2 figures

Photonic crystals doped with resonant atoms allow for uniquely advantageous nonlinear modes of optical propagation: (a) Self-induced transparency (SIT) solitons and multi-dimensional localized "bullets" propagating at photonic band gap frequencies. These modes can exist even at ultraweak intensities (few photons) and therefore differ substantially either from solitons in Kerr-nonlinear photonic crystals or from SIT solitons in uniform media. (b) Cross-coupling between pulses exhibiting electromagnetically induced transparency (EIT) and SIT gap solitons. We show that extremely strong correlations (giant cross-phase modulation) can be formed between the two pulses. These features may find applications in high-fidelity classical and quantum optical communications., Comment: 11 pages, 7 figures, to appear in JOSA-B

Applying the recently developed formalism of quantum-state transformation at absorbing dielectric four-port devices [L.~Kn\"oll, S.~Scheel, E.~Schmidt, D.-G.~Welsch, and A.V.~Chizhov, Phys. Rev. A {\bf 59}, 4716 (1999)], we calculate the quantum state of the outgoing modes of a two-mode squeezed vacuum transmitted through optical fibers of given extinction coefficients. Using the Peres--Horodecki separability criterion for continuous variable systems [R.~Simon, Phys. Rev. Lett. {\bf 84}, 2726 (2000)], we compute the maximal length of transmission of a two-mode squeezed vacuum through an absorbing system for which the transmitted state is still inseparable. Further, we calculate the maximal gain for which inseparability can be observed in an amplifying setup. Finally, we estimate an upper bound of the entanglement preserved after transmission through an absorbing system. The results show that the characteristic length of entanglement degradation drastically decreases with increasing strength of squeezing., Comment: Paper presented at the International Conference on Quantum Optics and VIII Seminar on Quantum Optics, Raubichi, Belarus, May 28-31, 2000, 11 pages, LaTeX2e, 4 eps figures

Dielectric four-port devices play an important role in optical quantum information processing. Since for causality reasons the permittivity is a complex function of frequency, dielectrics are typical examples of noisy quantum channels, which cannot preserve quantum coherence. To study the effects of quantum decoherence, we start from the quantized electromagnetic field in an arbitrary Kramers--Kronig dielectric of given complex permittivity and construct the transformation relating the output quantum state to the input quantum state, without placing restrictions on the frequency. We apply the formalism to some typical examples in quantum communication. In particular we show that for entangled qubits the Bell-basis states $|\Psi^\pm>$ are more robust against decoherence than the states $|\Phi^\pm>$., Comment: 12 pages, revtex, 10 eps figures, minor corrections in Appendix

The content of phase information of an arbitrary phase--sensitive measurement is evaluated using the maximum likelihood estimation. The phase distribution is characterized by the relative entropy--a nonlinear functional of input quantum state. As an explicit example the multiple measurement of quadrature operator is interpreted as quantum phase detection achieving the ultimate resolution predicted by the Fisher information., Comment: 4 pages, Revtex, 2 figures .pcx uuencode