Direct measurements of entanglement entropy in one-dimensional bosonic systems RUICHAO MA, ERIC TAI, ALEXANDER LUKIN, PHILIPP PREISS, MATTHEW RISPOLI, RAJIBUL ISLAM, MARKUS GREINER, Harvard University | The presence of large-scale entanglement is a dening
characteristic of exotic quantum phases of matter. However, its experimental verication is an outstanding challenge in condensed matter physics. Within small quantum information processing units, entanglement may be detected via resource-intensive state tomography or class-specic entanglement witnesses. Here, we demonstrate a novel approach to the measurement of entanglement entropy of any bosonic system, using a quantum gas microscope with tailored potential landscapes. We extend the concept of Hong-Ou-Mandel interference from two particles to many-body states. Interfering two copies of identically prepared states measures the quantum mechanical purity of the system and its subsystems, placing bounds on the entanglement entropy. We apply this technique to observe the entanglement dynamics in a few-particle quench of a bosonic system. Our protocol may be applied to any many-body state and provides a new platform for the characterization of strongly correlated states in optical
characteristic of exotic quantum phases of matter. However, its experimental verication is an outstanding challenge in condensed matter physics. Within small quantum information processing units, entanglement may be detected via resource-intensive state tomography or class-specic entanglement witnesses. Here, we demonstrate a novel approach to the measurement of entanglement entropy of any bosonic system, using a quantum gas microscope with tailored potential landscapes. We extend the concept of Hong-Ou-Mandel interference from two particles to many-body states. Interfering two copies of identically prepared states measures the quantum mechanical purity of the system and its subsystems, placing bounds on the entanglement entropy. We apply this technique to observe the entanglement dynamics in a few-particle quench of a bosonic system. Our protocol may be applied to any many-body state and provides a new platform for the characterization of strongly correlated states in optical
Entanglement is not only fundamental for understanding multipartite quantum systems but also generally useful for quantum information applications. Despite much effort devoted so far, little is known about minimal resources for detecting entanglement and also comparisons to tomography which reveals the full characterization. Here, we show that all entangled states can in general be detected in an experimental scheme that estimates the fidelity of two pure quantum states. An experimental proposal is presented with a single Hong-Ou-Mandel interferometry in which only two detectors are applied regardless of the dimensions or the number of modes of quantum systems. This shows measurement settings for entanglement detection are in general inequivalent to tomography: the number of detectors in quantum tomography increases with the dimensions and the modes whereas it is not the case in estimation of fidelity which detects entangled states.
Despite its ubiquity in quantum computation and quantum information, a universally applicable definition of quantum entanglement remains elusive. The challenge is further accentuated when entanglement is associated with other key themes, e.g., quantum interference and quantum statistics. Here, we introduce two novel motifs that characterize the interplay of entanglement and quantum statistics: an 'entanglement pointer' and a 'statistics-induced entanglement entropy'. The two provide a quantitative description of the statistics-induced entanglement: (i) they are finite only in the presence of quantum entanglement underlined by quantum statistics; (ii) their explicit form depends on the quantum statistics of the particles (e.g., fermions, bosons, anyons). We have experimentally implemented these ideas by employing an electronic Hong-Ou-Mandel interferometer fed by two highly diluted electron beams in an integer quantum Hall platform. Performing measurements of auto-correlation and cross-correlation of current fluctuations of the scattered beams (following 'collisions'), we quantify the statistics-induced entanglement by experimentally accessing the entanglement pointer and the statistics-induced entanglement entropy. Our theoretical and experimental approaches pave the way to study entanglement in various correlated platforms, e.g., those involving anyonic Abelian and non-Abelian states.
Despite its ubiquity in quantum computation and quantum information, a universally applicable definition of quantum entanglement remains elusive. The challenge is further accentuated when entanglement is associated with other key themes, e.g., quantum interference and quantum statistics. Here, we introduce two novel motifs that characterize the interplay of entanglement and quantum statistics: an 'entanglement pointer' and a 'statistics-induced entanglement entropy'. The two provide a quantitative description of the statistics-induced entanglement: (i) they are finite only in the presence of quantum entanglement underlined by quantum statistics and (ii) their explicit form depends on the quantum statistics of the particles (e.g., fermions, bosons, and anyons). We have experimentally implemented these ideas by employing an electronic Hong-Ou-Mandel interferometer fed by two highly diluted electron beams in an integer quantum Hall platform. Performing measurements of auto-correlation and cross-correlation of current fluctuations of the scattered beams (following 'collisions'), we quantify the statistics-induced entanglement by experimentally accessing the entanglement pointer and the statistics-induced entanglement entropy. Our theoretical and experimental approaches pave the way to study entanglement in various correlated platforms, e.g., those involving anyonic Abelian and non-Abelian states.
Entanglement is a fundamental resource for quantum information processing [1-3], its applications including scalable quantum communication, secure quantum key distribution protocols for cryptography, and exponential speedup of quantum algorithms. It occurs naturally in manybody systems at low temperatures: This makes cold atoms good candidates to provide entangled states involving a large number of particles. For realizing and manipulating such states, an essential task is quantifying the actual amount of entanglement contained in the created state before using it for quantum information protocols. However, this task represents a major challenge, as it requires either full state tomography, scaling exponentially in the system size, or the assumption of unverified system characteristics such as its Hamiltonian or temperature. In this experiment [4], we obtain a quantification of multipartite entanglement from readily accessible measurements - that is, time-of-flight atomic density distribution - based on a recent proposal [5]. We directly observe and quantify the multipartite spatial entanglement between the sites of a periodic optical potential (optical lattice) that hosts massive bosonic particles. We characterize its behaviour when crossing the superfluid-Mott insulator transition and when varying temperature, demonstrating the robustness of our method. References [1] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press (Cambridge, 2000). [2]R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865-942 (2009). [3]O. Göhne and G. Tóth, Entanglement detection, Physics Reports 474, 1-75 (2009). [4]M. Cramer, A. Bernard, N. Fabbri, L. Fallani, C. Fort, S. Rosi, F. Caruso, M. Inguscio, and M. B. Plenio, Entanglement of bosons in optical lattices, E-print arXiv:1302.4897 [5]M. Cramer, M. B. Plenio, and H. Wunderlich, Measuring entanglement in condensed matter systems, Phys. Rev. Lett. 106, 020401 (2011).
Experiments with ultracold atoms in optical lattices provide outstanding opportunities to realize exotic quantum states due to a high degree of tunability and control. In this thesis, I present experiments that extend this control from global parameters to the level of individual particles. \n\nUsing a quantum gas microscope for 87Rb, we have developed a single-site addressing scheme based on digital amplitude holograms. The system self-corrects for aberrations in the imaging setup and creates arbitrary beam profiles. We are thus able to shape optical potentials on the scale of single lattice sites and control the dynamics of individual atoms. \n\nWe study the role of quantum statistics and interactions in the Bose-Hubbard model on the fundamental level of two particles. Bosonic quantum statistics are apparent in the Hong-Ou-Mandel interference of massive particles, which we observe in tailored double-well potentials. These underlying statistics, in combination with tunable repulsive interactions, dominate the dynamics in single- and two-particle quantum walks. We observe highly coherent position-space Bloch oscillations, bosonic bunching in Hanbury Brown-Twiss interference and the fermionization of strongly interacting bosons.\n\nMany-body states of indistinguishable quantum particles are characterized by large-scale spatial entanglement, which is difficult to detect in itinerant systems. Here, we extend the concept of Hong-Ou-Mandel interference from individual particles to many-body states to directly quantify entanglement entropy. We perform collective measurements on two copies of a quantum state and detect entanglement entropy through many-body interference. We measure the second order Rényi entropy in small Bose-Hubbard systems and detect the buildup of spatial entanglement across the superfluid-insulator transition.\n\nOur experiments open new opportunities for the single-particle-resolved preparation and characterization of many-body quantum states.