Abstract

Light enables manipulating many-body states of matter, and atoms trapped in optical lattices are a prominent example. However, quantum properties of light are completely neglected in all quantum gas experiments. Extending methods of quantum optics to many-body physics will enable phenomena unobtainable in classical optical setups. We show how using the quantum optical feedback creates strong correlations in bosonic and fermionic systems. It balances two competing processes, originating from different fields: quantum backaction of weak optical measurement and many-body dynamics, resulting in stabilized density waves and antiferromagnetic and NOON states. Our approach is extendable to other systems promising for quantum technologies.

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2016 (14)

G. Mazzucchi, W. Kozlowski, S. F. Caballero-Benitez, T. J. Elliott, and I. B. Mekhov, “Quantum measurement-induced dynamics of many-body ultracold bosonic and fermionic systems in optical lattices,” Phys. Rev. A 93, 023632 (2016).
[Crossref]

R. Landig, L. Hruby, N. Dogra, M. Landini, R. Mottl, T. Donner, and T. Esslinger, “Quantum phases emerging from competing short-and long-range interactions in an optical lattice,” Nature 532, 476–479 (2016).
[Crossref]

S. F. Caballero-Benitez, G. Mazzucchi, and I. B. Mekhov, “Quantum simulators based on the global collective light-matter interaction,” Phys. Rev. A 93, 063632 (2016).
[Crossref]

T. C. White, J. Y. Mutus, J. Dressel, J. Kelly, R. Barends, E. Jeffrey, D. Sank, A. Megrant, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, I.-C. Hoi, C. Neill, P. J. J. O’Malley, P. Roushan, A. Vainsencher, J. Wenner, A. N. Korotkov, and J. M. Martinis, “Preserving entanglement during weak measurement demonstrated with a violation of the Bell–Leggett–Garg inequality,” Npj Quant. Inf. 2, 15022 (2016).
[Crossref]

T. Nitsche, F. Elster, J. Novotný, A. Gábris, I. Jex, S. Barkhofen, and C. Silberhorn, “Quantum walks with dynamical control: graph engineering, initial state preparation and state transfer,” New J. Phys. 18, 063017 (2016).
[Crossref]

D. Oren, Y. Shechtman, M. Mutzafi, Y. C. Eldar, and M. Segev, “Sparsity-based recovery of three-photon quantum states from two-fold correlations,” Optica 3, 226–232 (2016).
[Crossref]

M. Mitrano, A. Cantaluppi, D. Nicoletti, S. Kaiser, A. Perucchi, S. Lupi, P. Di Pietro, D. Pontiroli, M. Riccò, S. R. Clark, D. Jaksch, and A. Cavalleri, “Possible light-induced superconductivity in K3C60 at high temperature,” Nature 530, 461–464 (2016).
[Crossref]

G. Mazzucchi, W. Kozlowski, S. F. Caballero-Benitez, and I. B. Mekhov, “Collective dynamics of multimode bosonic systems induced by weak quantum measurement,” New J. Phys. 18, 73017 (2016).
[Crossref]

W. Kozlowski, S. F. Caballero-Benitez, and I. B. Mekhov, “Non-Hermitian dynamics in the quantum Zeno limit,” Phys. Rev. A 94, 012123 (2016).
[Crossref]

G. Mazzucchi, S. F. Caballero-Benitez, and I. B. Mekhov, “Quantum measurement-induced antiferromagnetic order and density modulations in ultracold Fermi gases in optical lattices,” Sci. Rep. 6, 31196 (2016).
[Crossref]

A. Holleczek, O. Barter, A. Rubenok, J. Dilley, P. B. Nisbet-Jones, G. Langfahl-Klabes, G. D. Marshall, C. Sparrow, J. L. O’Brien, K. Poulios, and A. Kuhn, “Photonic quantum logic with narrowband light from single atoms,” Phys. Rev. Lett. 117, 023602 (2016).
[Crossref]

R. P. Marchildon and A. S. Helmy, “Dispersion-enabled quantum state control in integrated photonics,” Optica 3, 243–251 (2016).
[Crossref]

M. Minkov and V. Savona, “Haldane quantum Hall effect for light in a dynamically modulated array of resonators,” Optica 3, 200–206 (2016).
[Crossref]

G. Angelatos and S. Hughes, “Polariton waveguides from a quantum dot chain in a photonic crystal waveguide: an architecture for waveguide quantum electrodynamics,” Optica 3, 370–376 (2016).
[Crossref]

2015 (16)

P. Schauß, J. Zeiher, T. Fukuhara, S. Hild, M. Cheneau, T. Macr, T. Pohl, I. Bloch, and C. Gross, “Crystallization in Ising quantum magnets,” Science 347, 1455–1458 (2015).
[Crossref]

C. Budroni, G. Vitagliano, G. Colangelo, R. J. Sewell, O. Gühne, G. Toth, and M. Mitchell, “Quantum nondemolition measurement enables macroscopic Leggett-Garg tests,” Phys. Rev. Lett. 115, 200403 (2015).
[Crossref]

S. Denny, S. Clark, Y. Laplace, A. Cavalleri, and D. Jaksch, “Proposed parametric cooling of bilayer cuprate superconductors by terahertz excitation,” Phys. Rev. Lett. 114, 137001 (2015).
[Crossref]

G. Kurizki, P. Bertet, Y. Kubo, K. Mølmer, D. Petrosyan, P. Rabl, and J. Schmiedmayer, “Quantum technologies with hybrid systems,” Proc. Natl. Acad. Sci. U.S.A. 112, 3866–3873 (2015).
[Crossref]

R. Landig, F. Brennecke, R. Mottl, T. Donner, and T. Esslinger, “Measuring the dynamic structure factor of a quantum gas undergoing a structural phase transition,” Nat. Commun. 6, 7046 (2015).
[Crossref]

T. J. Elliott, W. Kozlowski, S. F. Caballero Benitez, and I. B. Mekhov, “Multipartite entangled spatial modes of ultracold atoms generated and controlled by quantum measurement,” Phys. Rev. Lett. 114, 113604 (2015).
[Crossref]

B. Brecht, D. V. Reddy, C. Silberhorn, and M. Raymer, “Photon temporal modes: a complete framework for quantum information science,” Phys. Rev. X 5, 041017 (2015).
[Crossref]

F. Elster, S. Barkhofen, T. Nitsche, J. Novotný, A. Gábris, I. Jex, and C. Silberhorn, “Quantum walk coherences on a dynamical percolation graph,” Sci. Rep. 5, 13495 (2015).
[Crossref]

S. F. Caballero-Benitez and I. B. Mekhov, “Quantum optical lattices for emergent many-body phases of ultracold atoms,” Phys. Rev. Lett. 115, 243604 (2015).
[Crossref]

S. F. Caballero-Benitez and I. B. Mekhov, “Quantum properties of light scattered from structured many-body phases of ultracold atoms in quantum optical lattices,” New J. Phys. 17, 123023 (2015).
[Crossref]

J. Klinder, H. Keßler, M. R. Bakhtiari, M. Thorwart, and A. Hemmerich, “Observation of a superradiant Mott insulator in the Dicke-Hubbard model,” Phys. Rev. Lett. 115, 230403 (2015).
[Crossref]

R. McConnell, H. Zhang, J. Hu, S. Cuk, and V. Vuletic, “Entanglement with negative Wigner function of almost 3,000 atoms heralded by one photon,” Nature 519, 439–442 (2015).
[Crossref]

T. Rybarczyk, B. Peaudecerf, M. Penasa, S. Gerlich, B. Julsgaard, K. Mølmer, S. Gleyzes, M. Brune, J. Raimond, S. Haroche, and I. Dotsenko, “Forward-backward analysis of the photon-number evolution in a cavity,” Phys. Rev. A 91, 062116 (2015).
[Crossref]

T. J. Elliott, G. Mazzucchi, W. Kozlowski, S. F. Caballero-Benitez, and I. B. Mekhov, “Probing and manipulating fermionic and bosonic quantum gases with quantum light,” Atoms 3, 392–406 (2015).
[Crossref]

Y. Ashida and M. Ueda, “Diffraction-unlimited position measurement of ultracold atoms in an optical lattice,” Phys. Rev. Lett. 115, 095301 (2015).
[Crossref]

W. Kozlowski, S. F. Caballero-Benitez, and I. B. Mekhov, “Probing matter-field and atom-number correlations in optical lattices by global nondestructive addressing,” Phys. Rev. A 92, 013613 (2015).
[Crossref]

2014 (8)

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014).
[Crossref]

M. K. Pedersen, J. J. W. H. Sorensen, M. C. Tichy, and J. F. Sherson, “Many-body state engineering using measurements and fixed unitary dynamics,” New J. Phys. 16, 113038 (2014).
[Crossref]

M. D. Lee and J. Ruostekoski, “Classical stochastic measurement trajectories: bosonic atomic gases in an optical cavity and quantum measurement backaction,” Phys. Rev. A 90, 023628 (2014).
[Crossref]

D. Ivanov and T. Ivanova, “Feedback-enhanced self-organization of atoms in an optical cavity,” JETP Lett. 100, 481–485 (2014).
[Crossref]

B. Rogers, M. Paternostro, J. F. Sherson, and G. De Chiara, “Characterization of Bose-Hubbard models with quantum nondemolition measurements,” Phys. Rev. A 90, 043618 (2014).
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D. Nicoletti, E. Casandruc, Y. Laplace, V. Khanna, C. R. Hunt, S. Kaiser, S. Dhesi, G. Gu, J. Hill, and A. Cavalleri, “Optically induced superconductivity in striped La2-x Bax CuO4 by polarization-selective excitation in the near infrared,” Phys. Rev. B 90, 100503 (2014).
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T. Eichelkraut, C. Vetter, A. Perez-Leija, H. Moya-Cessa, D. N. Christodoulides, and A. Szameit, “Coherent random walks in free space,” Optica 1, 268–271 (2014).
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H. Keßler, J. Klinder, M. Wolke, and A. Hemmerich, “Steering matter wave superradiance with an ultranarrow-band optical cavity,” Phys. Rev. Lett. 113, 070404 (2014).
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2013 (9)

J.-M. Pirkkalainen, S. Cho, J. Li, G. Paraoanu, P. Hakonen, and M. Sillanpää, “Hybrid circuit cavity quantum electrodynamics with a micromechanical resonator,” Nature 494, 211–215 (2013).
[Crossref]

I. B. Mekhov, “Quantum non-demolition detection of polar molecule complexes: dimers, trimers, tetramers,” Laser Phys. 23, 015501 (2013).
[Crossref]

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X.-M. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, and J. C. Gates, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
[Crossref]

S. Bux, H. Tomczyk, D. Schmidt, P. W. Courteille, N. Piovella, and C. Zimmermann, “Control of matter-wave superradiance with a high-finesse ring cavity,” Phys. Rev. A 87, 023607 (2013).
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P. Hauke, R. J. Sewell, M. W. Mitchell, and M. Lewenstein, “Quantum control of spin correlations in ultracold lattice gases,” Phys. Rev. A 87, 021601 (2013).
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B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon Schrödinger cat states,” Science 342, 607–610 (2013).
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A. Reiserer, S. Ritter, and G. Rempe, “Nondestructive detection of an optical photon,” Science 342, 1349–1351 (2013).
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H. Ritsch, P. Domokos, F. Brennecke, and T. Esslinger, “Cold atoms in cavity-generated dynamical optical potentials,” Rev. Mod. Phys. 85, 553–601 (2013).
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W. Niedenzu, S. Schütz, H. Habibian, G. Morigi, and H. Ritsch, “Seeding patterns for self-organization of photons and atoms,” Phys. Rev. A 88, 033830 (2013).
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2012 (3)

I. B. Mekhov and H. Ritsch, “Quantum optics with ultracold quantum gases: towards the full quantum regime of the light-matter interaction,” J. Phys. B 45, 102001 (2012).
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J. Meineke, J.-P. Brantut, D. Stadler, T. Müller, H. Moritz, and T. Esslinger, “Interferometric measurement of local spin fluctuations in a quantum gas,” Nat. Phys. 8, 455–459 (2012).
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C. Sanner, E. J. Su, W. Huang, A. Keshet, J. Gillen, and W. Ketterle, “Correlations and pair formation in a repulsively interacting Fermi gas,” Phys. Rev. Lett. 108, 240404 (2012).
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2011 (4)

I. B. Mekhov and H. Ritsch, “Atom state evolution and collapse in ultracold gases during light scattering into a cavity,” Laser Phys. 21, 1486–1490 (2011).
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G. Paraoanu, “Generalized partial measurements,” Europhys. Lett. 93, 64002 (2011).
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M. Paternostro, “Engineering nonclassicality in a mechanical system through photon subtraction,” Phys. Rev. Lett. 106, 183601 (2011).
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C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, and J. M. Raimond, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
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2010 (2)

A. Palacios-Laloy, F. Mallet, F. Nguyen, P. Bertet, D. Vion, D. Esteve, and A. N. Korotkov, “Experimental violation of a Bell’s inequality in time with weak measurement,” Nat. Phys. 6, 442–447 (2010).
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I. B. Mekhov and H. Ritsch, “Quantum optical measurements in ultracold gases: macroscopic Bose Einstein condensates,” Laser Phys. 20, 694–699 (2010).
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2009 (4)

I. B. Mekhov and H. Ritsch, “Quantum optics with quantum gases,” Laser Phys. 19, 610–615 (2009).
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I. B. Mekhov and H. Ritsch, “Quantum optics with quantum gases: controlled state reduction by designed light scattering,” Phys. Rev. A 80, 013604 (2009).
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T. Roscilde, M. Rodrguez, K. Eckert, O. Romero-Isart, M. Lewenstein, E. Polzik, and A. Sanpera, “Quantum polarization spectroscopy of correlations in attractive fermionic gases,” New J. Phys. 11, 055041 (2009).
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W. Chen and P. Meystre, “Cavity QED characterization of many-body atomic states in double-well potentials: role of dissipation,” Phys. Rev. A 79, 043801 (2009).
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2007 (2)

K. Eckert, O. Romero-Isart, M. Rodriguez, M. Lewenstein, E. S. Polzik, and A. Sanpera, “Quantum non-demolition detection of strongly correlated systems,” Nat. Phys. 4, 50–54 (2007).
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I. B. Mekhov, C. Maschler, and H. Ritsch, “Probing quantum phases of ultracold atoms in optical lattices by transmission spectra in cavity quantum electrodynamics,” Nat. Phys. 3, 319–323 (2007).
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2006 (1)

J. Gambetta, A. Blais, D. I. Schuster, A. Wallraff, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Qubit-photon interactions in a cavity: measurement-induced dephasing and number splitting,” Phys. Rev. A 74, 042318 (2006).
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2003 (1)

H. Büchler, G. Blatter, and W. Zwerger, “Commensurate-incommensurate transition of cold atoms in an optical lattice,” Phys. Rev. Lett. 90, 130401 (2003).
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1999 (1)

M. G. Moore, O. Zobay, and P. Meystre, “Quantum optics of a Bose-Einstein condensate coupled to a quantized light field,” Phys. Rev. A 60, 1491–1506 (1999).
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C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, and J. M. Raimond, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
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Y. Ashida and M. Ueda, “Diffraction-unlimited position measurement of ultracold atoms in an optical lattice,” Phys. Rev. Lett. 115, 095301 (2015).
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M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014).
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J. Klinder, H. Keßler, M. R. Bakhtiari, M. Thorwart, and A. Hemmerich, “Observation of a superradiant Mott insulator in the Dicke-Hubbard model,” Phys. Rev. Lett. 115, 230403 (2015).
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T. C. White, J. Y. Mutus, J. Dressel, J. Kelly, R. Barends, E. Jeffrey, D. Sank, A. Megrant, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, I.-C. Hoi, C. Neill, P. J. J. O’Malley, P. Roushan, A. Vainsencher, J. Wenner, A. N. Korotkov, and J. M. Martinis, “Preserving entanglement during weak measurement demonstrated with a violation of the Bell–Leggett–Garg inequality,” Npj Quant. Inf. 2, 15022 (2016).
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T. Nitsche, F. Elster, J. Novotný, A. Gábris, I. Jex, S. Barkhofen, and C. Silberhorn, “Quantum walks with dynamical control: graph engineering, initial state preparation and state transfer,” New J. Phys. 18, 063017 (2016).
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J. Zeiher, R. van Bijnen, P. Schauß, S. Hild, J.-Y. Choi, T. Pohl, I. Bloch, and C. Gross, “Many-body interferometry of a Rydberg-dressed spin lattice,” Nat. Phys. (to be published).
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J. Meineke, J.-P. Brantut, D. Stadler, T. Müller, H. Moritz, and T. Esslinger, “Interferometric measurement of local spin fluctuations in a quantum gas,” Nat. Phys. 8, 455–459 (2012).
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B. Brecht, D. V. Reddy, C. Silberhorn, and M. Raymer, “Photon temporal modes: a complete framework for quantum information science,” Phys. Rev. X 5, 041017 (2015).
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R. Landig, F. Brennecke, R. Mottl, T. Donner, and T. Esslinger, “Measuring the dynamic structure factor of a quantum gas undergoing a structural phase transition,” Nat. Commun. 6, 7046 (2015).
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H. Ritsch, P. Domokos, F. Brennecke, and T. Esslinger, “Cold atoms in cavity-generated dynamical optical potentials,” Rev. Mod. Phys. 85, 553–601 (2013).
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C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, and J. M. Raimond, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
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M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: a direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
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C. Budroni, G. Vitagliano, G. Colangelo, R. J. Sewell, O. Gühne, G. Toth, and M. Mitchell, “Quantum nondemolition measurement enables macroscopic Leggett-Garg tests,” Phys. Rev. Lett. 115, 200403 (2015).
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S. Bux, H. Tomczyk, D. Schmidt, P. W. Courteille, N. Piovella, and C. Zimmermann, “Control of matter-wave superradiance with a high-finesse ring cavity,” Phys. Rev. A 87, 023607 (2013).
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T. J. Elliott, W. Kozlowski, S. F. Caballero Benitez, and I. B. Mekhov, “Multipartite entangled spatial modes of ultracold atoms generated and controlled by quantum measurement,” Phys. Rev. Lett. 114, 113604 (2015).
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G. Mazzucchi, W. Kozlowski, S. F. Caballero-Benitez, and I. B. Mekhov, “Collective dynamics of multimode bosonic systems induced by weak quantum measurement,” New J. Phys. 18, 73017 (2016).
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W. Kozlowski, S. F. Caballero-Benitez, and I. B. Mekhov, “Non-Hermitian dynamics in the quantum Zeno limit,” Phys. Rev. A 94, 012123 (2016).
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G. Mazzucchi, W. Kozlowski, S. F. Caballero-Benitez, T. J. Elliott, and I. B. Mekhov, “Quantum measurement-induced dynamics of many-body ultracold bosonic and fermionic systems in optical lattices,” Phys. Rev. A 93, 023632 (2016).
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S. F. Caballero-Benitez, G. Mazzucchi, and I. B. Mekhov, “Quantum simulators based on the global collective light-matter interaction,” Phys. Rev. A 93, 063632 (2016).
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G. Mazzucchi, S. F. Caballero-Benitez, and I. B. Mekhov, “Quantum measurement-induced antiferromagnetic order and density modulations in ultracold Fermi gases in optical lattices,” Sci. Rep. 6, 31196 (2016).
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S. F. Caballero-Benitez and I. B. Mekhov, “Quantum optical lattices for emergent many-body phases of ultracold atoms,” Phys. Rev. Lett. 115, 243604 (2015).
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S. F. Caballero-Benitez and I. B. Mekhov, “Quantum properties of light scattered from structured many-body phases of ultracold atoms in quantum optical lattices,” New J. Phys. 17, 123023 (2015).
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W. Kozlowski, S. F. Caballero-Benitez, and I. B. Mekhov, “Probing matter-field and atom-number correlations in optical lattices by global nondestructive addressing,” Phys. Rev. A 92, 013613 (2015).
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T. J. Elliott, G. Mazzucchi, W. Kozlowski, S. F. Caballero-Benitez, and I. B. Mekhov, “Probing and manipulating fermionic and bosonic quantum gases with quantum light,” Atoms 3, 392–406 (2015).
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S. F. Caballero-Benitez and I. B. Mekhov, “Bond order via light-induced synthetic many-body interactions of ultracold atoms in optical lattices,” arXiv:1604.02563 (2016).

W. Kozlowski, S. F. Caballero-Benitez, and I. B. Mekhov, “Quantum state reduction by matter-phase-related measurements in optical lattices,” arXiv:1605.06000 (2016).

Campbell, B.

T. C. White, J. Y. Mutus, J. Dressel, J. Kelly, R. Barends, E. Jeffrey, D. Sank, A. Megrant, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, I.-C. Hoi, C. Neill, P. J. J. O’Malley, P. Roushan, A. Vainsencher, J. Wenner, A. N. Korotkov, and J. M. Martinis, “Preserving entanglement during weak measurement demonstrated with a violation of the Bell–Leggett–Garg inequality,” Npj Quant. Inf. 2, 15022 (2016).
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M. Mitrano, A. Cantaluppi, D. Nicoletti, S. Kaiser, A. Perucchi, S. Lupi, P. Di Pietro, D. Pontiroli, M. Riccò, S. R. Clark, D. Jaksch, and A. Cavalleri, “Possible light-induced superconductivity in K3C60 at high temperature,” Nature 530, 461–464 (2016).
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D. Nicoletti, E. Casandruc, Y. Laplace, V. Khanna, C. R. Hunt, S. Kaiser, S. Dhesi, G. Gu, J. Hill, and A. Cavalleri, “Optically induced superconductivity in striped La2-x Bax CuO4 by polarization-selective excitation in the near infrared,” Phys. Rev. B 90, 100503 (2014).
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M. Mitrano, A. Cantaluppi, D. Nicoletti, S. Kaiser, A. Perucchi, S. Lupi, P. Di Pietro, D. Pontiroli, M. Riccò, S. R. Clark, D. Jaksch, and A. Cavalleri, “Possible light-induced superconductivity in K3C60 at high temperature,” Nature 530, 461–464 (2016).
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S. Denny, S. Clark, Y. Laplace, A. Cavalleri, and D. Jaksch, “Proposed parametric cooling of bilayer cuprate superconductors by terahertz excitation,” Phys. Rev. Lett. 114, 137001 (2015).
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D. Nicoletti, E. Casandruc, Y. Laplace, V. Khanna, C. R. Hunt, S. Kaiser, S. Dhesi, G. Gu, J. Hill, and A. Cavalleri, “Optically induced superconductivity in striped La2-x Bax CuO4 by polarization-selective excitation in the near infrared,” Phys. Rev. B 90, 100503 (2014).
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W. Chen and P. Meystre, “Cavity QED characterization of many-body atomic states in double-well potentials: role of dissipation,” Phys. Rev. A 79, 043801 (2009).
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T. C. White, J. Y. Mutus, J. Dressel, J. Kelly, R. Barends, E. Jeffrey, D. Sank, A. Megrant, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, I.-C. Hoi, C. Neill, P. J. J. O’Malley, P. Roushan, A. Vainsencher, J. Wenner, A. N. Korotkov, and J. M. Martinis, “Preserving entanglement during weak measurement demonstrated with a violation of the Bell–Leggett–Garg inequality,” Npj Quant. Inf. 2, 15022 (2016).
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B. Rogers, M. Paternostro, J. F. Sherson, and G. De Chiara, “Characterization of Bose-Hubbard models with quantum nondemolition measurements,” Phys. Rev. A 90, 043618 (2014).
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S. Denny, S. Clark, Y. Laplace, A. Cavalleri, and D. Jaksch, “Proposed parametric cooling of bilayer cuprate superconductors by terahertz excitation,” Phys. Rev. Lett. 114, 137001 (2015).
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A. Holleczek, O. Barter, A. Rubenok, J. Dilley, P. B. Nisbet-Jones, G. Langfahl-Klabes, G. D. Marshall, C. Sparrow, J. L. O’Brien, K. Poulios, and A. Kuhn, “Photonic quantum logic with narrowband light from single atoms,” Phys. Rev. Lett. 117, 023602 (2016).
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Other (8)

M. Lewenstein, A. Sanpera, and V. Ahufinger, Ultracold Atoms in Optical Lattices: Simulating Quantum Many-Body Systems (Oxford University, 2012), p. 479.

S. F. Caballero-Benitez and I. B. Mekhov, “Bond order via light-induced synthetic many-body interactions of ultracold atoms in optical lattices,” arXiv:1604.02563 (2016).

S. Haroche and J.-M. Raimond, Exploring the Quantum: Atoms, Cavities, and Photons (Oxford University, 2006).

D. A. Ivanov, T. Y. Ivanova, and I. B. Mekhov, “Incoherent quantum feedback control of collective light scattering by Bose-Einstein condensates,” arXiv:1601.02230 (2016).

Q. Zhang, M. Lou, X. Li, J. L. Reno, W. Pan, J. D. Watson, M. J. Manfra, and J. Kono, “Collective, coherent, and ultrastrong coupling of 2D electrons with terahertz cavity photons,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2016), paper FTu3L.6.

J. Zeiher, R. van Bijnen, P. Schauß, S. Hild, J.-Y. Choi, T. Pohl, I. Bloch, and C. Gross, “Many-body interferometry of a Rydberg-dressed spin lattice,” Nat. Phys. (to be published).
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W. Kozlowski, S. F. Caballero-Benitez, and I. B. Mekhov, “Quantum state reduction by matter-phase-related measurements in optical lattices,” arXiv:1605.06000 (2016).

H. M. Wiseman and G. J. Milburn, Quantum Measurement and Control (Cambridge University, 2010).

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Figures (4)

Fig. 1.
Fig. 1. Experimental setup. Ultracold atoms are loaded in an optical lattice (OL) inside an optical cavity and probed with a coherent light beam (mode a0). The cavity enhances the light scattered orthogonally to a0, and the photons escaping it are detected (mode a1). Depending on the measurement outcome, a feedback (FB) loop with gain z is applied for modulating the depth of the optical lattice.
Fig. 2.
Fig. 2. Probability distribution of N^oddN^even for single quantum trajectories (Panels 1) and averages over 200 trajectories (Panels 2) for different values of the feedback gain z. Panel 3 shows the power spectrum of N^oddN^even averaged over 200 trajectories. In the absence of feedback [Panel (a), z=0] the oscillations of the population of the odd sites are visible only in a single trajectory. For z>zc [Panel (b), z=1.23zc] the imbalance between odd and even sites is frozen for each quantum trajectory and E[|F|2] does not have a strong peak, indicating that N^oddN^even does not oscillate. For z<zc the frequency of the oscillations can be tuned above [Panel (c), z=4zc] or below [Panel (d), z=0.8zc] the frequency defined by the tunneling amplitude J. Again, the oscillatory dynamics is visible only in a single quantum trajectory, and the average probability distribution spreads quickly. (N=100, γ/J=0.02, Jjj=(1)j, zc=0.0025).
Fig. 3.
Fig. 3. Effects of measurement and feedback detecting the photons scattered in the diffraction minimum. (a) Imbalance between odd and even sites as a function of the feedback strength. There is very good agreement between the numerical results and the analytic expression derived in the text. (b) Average power spectrum as a function of the feedback strength. The value of E[|F|2] presents a strong peak for z<zc, indicating that the trajectories are characterized by an oscillatory dynamics. The vertical dashed line marks z=zc. (N=100, γ/J=0.02, Jjj=(1)j, zc=0.0025).
Fig. 4.
Fig. 4. Effects of measurement and feedback probing the staggered magnetization in a fermionic system. (a) Square of the staggered magnetization as a function of the feedback strength (blue line) compared to the analytic formula (red line) for a fermionic system. Note that the two curves do not have the same behavior because the analytic solution assumes that M^S is a continuous variable while the numerical simulations are performed on a small system where M^S assumes only discrete values. (b) Steady state value of the probability distribution of M^S as a function of the feedback strength. The dashed line represents the theoretical prediction. The feedback loop stabilizes antiferromagnetic correlations. (N=N=4, γ/J=1, Jjj=(1)j, zc=1/128).

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

C=iΩ10a0iΔpκ
dρ^(t)={dN[eK(G[c^]+1)1]dtH[iH^0+12c^c^]}ρ^(t),
G[A^]ρ^=A^ρ^A^Tr[A^ρ^A^]ρ^,
H[A^]ρ^=A^ρ^+ρ^A^Tr[A^ρ^+ρ^A^],
Kρ^=i[zH^0,ρ^],
|ψ(t;Nph)n=2Nph[eiH^effΔtneizH^0c^]eiH^effΔt1|ψ0,
eiH^effΔtneizH^0ei(Δtnz)H^0c^c^Δtn/2.
J=4ERπ(V0ER)3/4exp(2V0ER),

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