Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems

Abstract

† These authors contributed equally to this work Quantum simulators are controllable quantum systems that can reproduce the dynamics of the system of interest, which are unfeasible for classical computers. Recent developments in quantum technology enable the precise control of individual quantum particles as required for studying complex quantum systems. Particularly, quantum simulators capable of simulating frustrated Heisenberg spin systems provide platforms for understanding exotic matter such as high-temperature superconductors. Here we report the analog quantum simulation of the ground-state wavefunction to probe arbitrary Heisenberg-type interactions among four spin-1/2 particles . Depending on the interaction strength, frustration within the system emerges such that the ground state evolves from a localized to a resonating valence-bond state. This spin-1/2 tetramer is created using the polarization states of four photons. The single-particle addressability and tunable measurement-induced interactions provide us insights into entanglement dynamics among individual particles. We directly extract ground-state energies and pair-wise quantum correlations to observe the monogamy of entanglement.During the past years, there has been an explosion of interest in quantum-enhanced technologies. The applications are many-fold and reach from quantum metrology[1] to quantum information processing [2]. In particular quantum computation has generated a lot of interest due to the discovery of quantum algorithms [3][4][5] which outperform classical ones. The first proposed application for which quantum computation can give an exponential enhancement over classical computation was suggested by Richard Feynman [6,7]. He considered a universal quantum mechanical simulator, which is a controllable quantum system that can be used to imitate other quantum systems, therefore being able to tackle problems that are intractable on classical computers. Since then the motivation to use a quantum simulator as a powerful tool to address the most important and difficult problems in multidisciplinary science has led to many theoretical proposals [8][9][10][11][12][13]. Vast technological developments allowed for recent realizations of such devices in atoms [14][15][16], trapped ions [17][18][19][20], single photons [21][22][23][24] and NMR [25,26]. The quantum simulation of strongly correlated quantum systems (e.g. frustrated spin systems) is of special interest and would provide new results that cannot be otherwise classically simulated [27].In order to manipulate and measure individual properties of microscopic quantum systems the complete control over all degrees of freedom for each particle is required. Typically, atoms in optical lattices [14] are used for realizing physical systems that can simulate various models in condensed-matter physics. The fact that the experimental addressability of single atoms in optical lattices remains very challenging [28][29][30] leads to the studies of bulk properties of the atomic ensemble (≈ 10 5 at...

Deterministic separation of arbitrary photon pair states in integrated quantum circuits

“…This occurs due to a change of sign in the mode operator transformation matrix elements [Eqn. (2)]. The sign change occurs smoothly without discontinuity, along a boundary where P I S = 0.…”

“…This is seen in along the line MΛ = π/2, where P S = 1 at any ∆ξ , which is again attributable to splitting ratio anti-symmetry. Λ=π/(2M) Figure 8 Visualization of the interplay between ∆ξ and MΛ in determining η (1) and η (2) , showing operating points where the coupler responds to the twin-photon state as a perfect 50:50 splitter (i and iii) and a perfect wavelength-demultiplexer (ii).…”

“…The state |Ψ evolves through a directional coupler with splitting ratio η σ (ω) and transforms according to Equation (2). It is assumed to remain in a pure state throughout this evolution.…”

“…For pair generation through SPDC from χ (2) nonlinearities, or spontaneous four-wave mixing (SFWM) from χ (3) nonlinearities, φ j αβ (ω 1 , ω 2 ) is determined by the parameters of the nonlinear interaction [29,30].…”

“…By harnessing fundamental quantum properties of light such as entanglement and superposition, quantum photonic technology has enabled new paradigms in secure communications [1], quantum simulation [2], and enhanced metrology [3]. Mapping quantum photonic technologies into an integrated on-chip setting has become an important task for overcoming the severe stability and scalability limitations of bulk-optics implementations.…”