Multimode States Research Articles

Quantum-network generation based on four-wave mixing

We present a scheme to realize versatile quantum networks by cascading several four-wave mixing (FWM) processes in warm rubidium vapors. FWM is an efficient $\chi^{(3)}$ nonlinear process, already used as a resource for multimode quantum state generation and which has been proved to be a promising candidate for applications to quantum information processing. We analyze theoretically the multimode output of cascaded FWM systems, derive its independent squeezed modes and show how, with phase controlled homodyne detection and digital post-processing, they can be turned into a versatile source of continuous variable cluster states.

Ghost Images with Four-Mode Entangled States

We demonstrate that the use of multimode entangled states of light fields can restore multiple ghost images of the object illuminated by radiation of one of the modes. The analysis, performed on the example of four-mode entangled light fields, is able to obtain three copies of ghost images.

Scanned Mask Imaging Ablative DPSS UV Laser Process for 2μm L/S RDL

Laser embedding conductors within a dielectric offers numerous advantages in fabricating redistribution layers (RDLs) for chip packages. Ablation of features down to 2μm L/S gives more routing space per layer and addresses the technology gap between semiconductor and PCB technologies. Microvias are made in the same process step as the circuitry, facilitating near padless vias further increasing the routing space available per layer. For a given package, this reduces the layer count and conductor path length required reducing the height profile of the package and improving signal integrity. Embedding the conductor can also improve its adhesion to the substrate and improve the co-planarity of subsequent layers in the build up. It also removes the need for the wet photochemistry associated with lithographic techniques. This presentation analyses the results of a novel UV, diode pumped solid state (DPSS), ablative mask imaging laser system for cost effective, high volume, 3D structuring of organic dielectrics. Two methods are widely used to micro-structure materials by laser: mask projection and direct write. Excimer lasers are typically used in mask projection systems, where their high pulse energy and low coherence make them well suited to imaging. These systems can achieve the required ablation quality with 2–3μm line width and space, however excimer lasers have a high capital cost and require regular and costly maintenance when compared with DPSS lasers. The high beam quality and lower pulse energy of DPSS lasers makes them better suited to a direct write approach. A galvanometer scan head used in conjunction with an f-theta scan lens can be used to scan a focused beam across a substrate. Since the pattern is defined by a CAD file, these systems are very flexible and thus appropriate for low volume prototyping. However, complicated control systems are required to accurately control the ablated depth, and constraints in the circuit design are imposed by the direct write approach. Also, because each feature is marked sequentially, the process time is proportional to the pattern complexity, which makes these tools prohibitively slow for high volume manufacture of the high density RDLs required in the next generation of device packages. This presentation outlines a scanned mask imaging system, wherein a low maintenance, cost efficient, frequency tripled, nanosecond, multimode UV solid state laser is used to illuminate a binary reticle. The multimode beam has an approximately Gaussian beam profile which is homogenised to form a square, flat top profile. A galvanometer scan head is used to raster scan the binary reticle. The reticle is subsequently imaged onto the substrate by a projection lens. Ablation of various features down to 2μm L/S in a variety of low K organic dielectrics is demonstrated. Accurate registration of pads with vias down to 5μm diameter highlights the feasibility of the process for high density RDLs and micro-vias for organic interposers. The process can achieve an ablation quality comparable to that of an excimer laser system, but with the advantage of significant cost saving and ease of maintenance in an industrial environment.

Entanglement-based continuous-variable quantum key distribution with multimode states and detectors

Secure quantum key distribution with multimode Gaussian entangled states and multimode homodyne detectors is proposed. In general the multimode character of both the sources of entanglement and the homodyne detectors can cause a security break even for a perfect channel when trusted parties are unaware of the detection structure. Taking into account the multimode structure and potential leakage of information from a homodyne detector reduces the loss of security to some extent. We suggest the symmetrization of the multimode sources of entanglement as an efficient method allowing us to fully recover the security irrespectively to multimode structure of the homodyne detectors. Further, we demonstrate that by increasing the number of the fluctuating but similar source modes the multimode protocol stabilizes the security of the quantum key distribution. The result opens the pathway towards quantum key distribution with multimode sources and detectors.

Asymmetric quantum hypothesis testing with Gaussian states

We consider the asymmetric formulation of quantum hypothesis testing, where two quantum hypotheses have different associated costs. In this problem, the aim is to minimize the probability of false negatives and the optimal performance is provided by the quantum Hoeffding bound. After a brief review of these notions, we show how this bound can be simplified for pure states. We then provide a general recipe for its computation in the case of multimode Gaussian states, also showing its connection with other easier-to-compute lower bounds. In particular, we provide analytical formulas and numerical results for important classes of one- and two-mode Gaussian states.

Hamiltonian design in readout from room-temperature Raman atomic memory.

We present an experimental demonstration of the Hamiltonian manipulation in light-atom interface in Raman-type warm rubidium-87 vapor atomic memory. By adjusting the detuning of the driving beam we varied the relative contributions of the Stokes and anti-Stokes scattering to the process of four-wave mixing which reads out a spatially multimode state of atomic memory. We measured the temporal evolution of the readout fields and the spatial intensity correlations between write-in and readout as a function of detuning with the use of an intensified camera. The correlation maps enabled us to resolve between the anti-Stokes and the Stokes scattering and to quantify their contributions. Our experimental results agree quantitatively with a simple, plane-wave theoretical model we provide. They allow for a simple interpretation of the coaction of the anti-Stokes and the Stokes scattering at the readout stage. The Stokes contribution yields additional, adjustable gain at the readout stage, albeit with inevitable extra noise. Here we provide a simple and useful framework to trace it and the results can be utilized in the existing atomic memories setups. Furthermore, the shown Hamiltonian manipulation offers a broad range of atom-light interfaces readily applicable in current and future quantum protocols with atomic ensembles.

Gaussian states and geometrically uniform symmetry

Quantum Gaussian states can be considered as the majority of the practical quantum states used in quantum communications and more generally in quantum information. Here we consider their properties in relation with the geometrically uniform symmetry, a property of quantum states that greatly simplifies the derivation of the optimal decision by means of the square root measurements. In a general framework of the $N$-mode Gaussian states we show the general properties of this symmetry and the application of the optimal quantum measurements. An application example is presented, to quantum communication systems employing pulse position modulation. We prove that the geometrically uniform symmetry can be applied to the general class of multimode Gaussian states.

Photon counts statistics of squeezed and multimode thermal states of light on multiplexed on–off detectors

Photon number resolving detectors can be highly useful for studying the statistics of multi-photon quantum states of light. In this work we study the counts statistics of different states of light measured on multiplexed on-off detectors. We put special emphasis on artificial nonclassical features of the statistics obtained. We show new ways to derive analytical formulas for counts statistics and their moments. Using our approach we are the first to derive statistics moments for multi-mode thermal states measured on multiplexed on-off detectors. We use them to determine empirical Mandel parameters and recently proposed subbinomial parameters suitable for tests of nonclassicality of the measured states. Additionally, we investigate subpoissonian and superbunching properties of the two-mode squeezed state measured on a pair of multiplexed detectors and we present results of the Fano factor and second-order correlation function for these states.

Multi-mode coherent states and multi-mode nonlinear coherent states

In this paper, three-mode nonlinear coherent states are introduced by using the complex solution of the equation q3 = 1. The photon-added or photon-subtracted three-mode nonlinear coherent states are shown to be three-mode nonlinear coherent states with different nonlinear functions. The Z3-graded parity coherent states are introduced as examples of three-mode nonlinear coherent states. Finally, multi-mode coherent states and multi-mode nonlinear coherent states are also constructed in a similar way.

Full characterization of a highly multimode entangled state embedded in an optical frequency comb using pulse shaping

An in-depth analysis of the correlation and entanglement properties of an optical frequency comb produced by a synchronously pumped optical parametric oscillator is presented, providing a unique capability for the continued development of specialized quantum networks within highly multimode structures.

Generation of multimode squeeze operators and multipartite entangled states for continuous variables

A scheme is presented for generating unitarily multimode field squeezing, cluster entanglement, and Greenberger-Horne-Zeilinger (GHZ) entanglement via cavity quantum electrodynamics. Through a suitable laser system, we are able to engineer a squeeze field operator decoupled from the atomic degrees of freedom, yielding a large squeeze parameter proportional to the number of atoms. The physical mechanism is attributed to the multiple four-photon processes and the dispersive atom-cavity-field interaction in large detuning systems.

Dispersion-induced dynamics of coupled modes in a semiconductor laser with saturable absorption

We present an experimental and theoretical study of modal nonlinear dynamics in a specially designed dual-mode semiconductor Fabry-Perot laser with a saturable absorber. At zero bias applied to the absorber section, we have found that with increasing device current, single mode self-pulsations evolve into a complex dynamical state where the total intensity experiences regular bursts of pulsations on a constant background. Spectrally resolved measurements reveal that in this state the individual modes of the device can follow highly symmetric but oppositely directed spiralling orbits. Using a generalization of the rate equation description of a semiconductor laser with saturable absorption to the multimode case, we show that these orbits appear as a consequence of the interplay between the material dispersion in the gain and absorber sections of the laser. Our results provide insights into the factors that determine the stability of multimode states in these systems, and they can inform the development of semiconductor mode-locked lasers with tailored spectra.

Realizable receivers for discriminating coherent and multicopy quantum states near the quantum limit

We derive the quantum limit on the error probability exponent for discriminating any $M$ multimode coherent states of light and show that it is four times that of an ideal heterodyne receiver for the same signal set. We then propose a receiver that achieves the quantum limit using auxiliary coherent-state fields, beam splitters, and single-photon detectors. The performance of the receiver is compared to standard measurements for various imaging and communication tasks. A related receiver for discriminating arbitrary multicopy pure quantum states is shown to achieve the $M$-ary quantum Chernoff exponent and does so using only local operations and classical communication.

The two-particle two-slit experiment

Identical two-particle interferometry provides a scenario where interference and exchange effects manifest at once. We present a detailed calculation of the detection patterns in the two-particle two-slit experiment by extending Feynman’s Gaussian slit approach to multi-mode states. We show the existence of two regimes depending on the mode distributions. In one of them we find a novel behavior for bosons, with detection patterns almost equal to those of distinguishable particles although the overlapping is large. As a byproduct of our analysis we conclude that the interaction at the diffraction grating is an efficient method to increase the initial overlapping. We propose a scheme, within the reach of present day technology, to experimentally verify our results.

The theory of stability, bistability, and instability in three-mode class-A lasers

Instability is an inevitable and common problem in all different kinds of lasers when they are oscillating in both single-and multi-mode states. Here, the stability conditions are investigated for a three-mode class-A laser. A set of linear equations is derived for the stable oscillation of the cavity central mode together with its left and right adjacent longitudinal modes. The coefficient determinant of stability equations is Hermitian and equal to zero for the roots of two diagonal arrays. In other words, the novelty of our work is to expand the stability coefficient determinant in terms of main diagonal arrays rather than for one row or one column. These diagonal roots lead to two lower and upper boundary curves in the form of a bifurcation. The lower boundary curve mimics the single-mode laser and delimits the instability region (with no above-threshold oscillating mode) from the bistability region (with two above-threshold oscillating modes). The upper boundary curve mimics the two-mode laser and delimits the bistability region from the stability region, in which all three-longitudinal modes are simultaneously oscillating in the above-threshold state.

Characterizing the nonclassicality of mesoscopic optical twin-beam states

We present a robust tool to analyze nonclassical properties of multimode twin-beam states in the mesoscopic photon-number domain. The measurements are performed by direct detection. The analysis exploits three different nonclassicality criteria for detected photons exhibiting complementary behavior in the explored intensity regime. Joint signal-idler photon-number distributions and quasidistributions of integrated intensities are determined and compared with the corresponding distributions of detected photons. Experimental conditions optimal for nonclassical properties of twin-beam states are identified.

Optimal sub-Poissonian light generation from twin beams by photon-number resolving detectors

We generate nonclassical conditional states by exploiting the quantum correlations of multimode twin-beam states endowed with a sizeable number of photons. A strong relation between the sub-shot-noise correlations exhibited by twin beams and the sub-Poissonian character of the conditional states is experimentally revealed, determining the optimal conditions for sub-Poissonian light generation.

Quantum probabilities of composite events in quantum measurements with multimode states

The problem of defining quantum probabilities of composite events is considered. This problem is of great importance for the theory of quantum measurements and for quantum decision theory, which is a part of measurement theory. We show that the Lüders probability of consecutive measurements is a transition probability between two quantum states and that this probability cannot be treated as a quantum extension of the classical conditional probability. The Wigner distribution is shown to be a weighted transition probability that cannot be accepted as a quantum extension of the classical joint probability. We suggest the definition of quantum joint probabilities by introducing composite events in multichannel measurements. The notion of measurements under uncertainty is defined. We demonstrate that the necessary condition for mode interference is the entanglement of the composite prospect together with the entanglement of the composite statistical state. As an illustration, we consider an example of a quantum game. Special attention is paid to the application of the approach to systems with multimode states, such as atoms, molecules, quantum dots, or trapped Bose-condensed atoms with several coherent modes.

Stabilizer information inequalities from phase space distributions

The Shannon entropy of a collection of random variables is subject to a number of constraints, the best-known examples being monotonicity and strong subadditivity. It remains an open question to decide which of these “laws of information theory” are also respected by the von Neumann entropy of many-body quantum states. In this article, we consider a toy version of this difficult problem by analyzing the von Neumann entropy of stabilizer states. We find that the von Neumann entropy of stabilizer states satisfies all balanced information inequalities that hold in the classical case. Our argument is built on the fact that stabilizer states have a classical model, provided by the discrete Wigner function: The phase-space entropy of the Wigner function corresponds directly to the von Neumann entropy of the state, which allows us to reduce to the classical case. Our result has a natural counterpart for multi-mode Gaussian states, which sheds some light on the general properties of the construction. We also discuss the relation of our results to recent work by Linden, Ruskai, and Winter [“The quantum entropy cone of stabiliser states,” e-print arXiv:1302.5453].

Exact solution and short-time dynamics of multimode Gaussian states embedded in a common non-Markovian environment

We investigate a system of N mutually coupled harmonic oscillators interacting with the same environment and derive the corresponding exact non-Markovian master equation using our introduced approach. We obtain an explicit formula for the covariance matrix of the evolved state by taking a Gaussian state as initial one. With this, we analyze the short-time non-Markovian dynamics of three-mode Gaussian state in high-temperature limit. Our results show that the short-time evolution behavior of bipartite entanglement for 1 × 2 bipartition is similar to that of genuine tripartite entanglement, while the 1 × 1 bipartition entanglement does not. It is also shown that there exists a threshold that makes the initial tri- and bipartite entanglement increase or decrease. For the squeezing degree of the initial state than this critical value, the entanglement is increased with the evolution time; otherwise it is decreased. Finally, we present a physical positivity criterion for the covariance matrix of the evolved state.