Probing quantum and thermal noise in an interacting many-body system

Hofferberth, Sebastian; Lesanovsky, Igor; Schumm, Thorsten; Imambekov, Adilet; Gritsev, Vladimir; Demler, Eugene; Schmiedmayer, Jörg

doi:10.1038/nphys941

Cited by 243 publications

(332 citation statements)

References 55 publications

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“…In future work, we intend to further investigate the damping of the spin dynamics and its connection to thermalization of isolated quantum systems subject to loss. Similar investigations are ongoing using one-dimensional condensate systems [30][31][32][33] , and it will be interesting to explore the similarities and differences in these completely different systems.…”

Section: Discussionmentioning

confidence: 95%

Non-equilibrium dynamics of an unstable quantum pendulum explored in a spin-1 Bose–Einstein condensate

et al. 2012

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A pendulum prepared perfectly inverted and motionless is a prototype of unstable equilibrium and corresponds to an unstable hyperbolic fixed point in the dynamical phase space. Here, we measure the non-equilibrium dynamics of a spin-1 Bose-Einstein condensate initialized as a minimum uncertainty spin-nematic state to a hyperbolic fixed point of the phase space. Quantum fluctuations lead to non-linear spin evolution along a separatrix and non-Gaussian probability distributions that are measured to be in good agreement with exact quantum calculations up to 0.25 s. At longer times, atomic loss due to the finite lifetime of the condensate leads to larger spin oscillation amplitudes, as orbits depart from the separatrix. This demonstrates how decoherence of a many-body system can result in apparent coherent behaviour. This experiment provides new avenues for studying macroscopic spin systems in the quantum limit and for investigations of important topics in non-equilibrium quantum dynamics.

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Section: Discussionmentioning

confidence: 95%

Non-equilibrium dynamics of an unstable quantum pendulum explored in a spin-1 Bose–Einstein condensate

et al. 2012

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“…The FCS provide a powerful tool to characterize many-body systems beyond average values [47], but so far has not been measured for the antiferromagnetic phase. Fig.…”

Section: (Methods)mentioning

confidence: 99%

“…For example, it has been used to observe the quantization of electrical charge in shot noise measurements [63], the observation of fractional charges in fractional quantum Hall systems [64][65][66], and was used to characterize prethermalization in an ultracold atomic setup [47,67,68]. Here we determine the FCS of the staggered magnetization operatorm z = 1 N i (−1) i 1 S S z i from an ab initio quantum Monte Carlo simulation of the antiferromagnetic Heisenberg model…”

Section: System Calibrationsmentioning

confidence: 99%

A cold-atom Fermi–Hubbard antiferromagnet

Mazurenko

Chiu

et al. 2017

Nature

730

689

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Many exotic phenomena in strongly correlated electron systems emerge from the interplay between spin and motional degrees of freedom [1, 2]. For example, doping an antiferromagnet gives rise to interesting phases including pseudogap states and high-temperature superconductors [3]. A promising route towards achieving a complete understanding of these materials begins with analytic and computational analysis of simplified models. Quantum simulation has recently emerged as a complementary approach towards understanding these models [4][5][6][7][8]. Ultracold fermions in optical lattices offer the potential to answer open questions on the lowtemperature regime of the doped Hubbard model [9][10][11], which is thought to capture essential aspects of the cuprate superconductor phase diagram but is numerically intractable in that parameter regime. Already, Mott-insulating phases and short-range antiferromagnetic correlations have been observed, but temperatures were too high to create an antiferromagnet [12][13][14][15]. A new perspective is afforded by quantum gas microscopy [16][17][18][19][20][21][22][23][24][25][26][27][28], which allows readout of magnetic correlations at the site-resolved level [25][26][27][28]. Here we report the realization of an antiferromagnet in a repulsively interacting Fermi gas on a 2D square lattice of approximately 80 sites. Using site-resolved imaging, we detect (finite-size) antiferromagnetic long-range order (LRO) through the development of a peak in the spin structure factor and the divergence of the correlation length that reaches the size of the system. At our lowest temperature of T/t = 0.25(2) we find strong order across the entire sample, where the staggered magnetization approaches the ground-state value. Our experimental platform enables doping away from half filling, where pseudogap states and stripe ordering are expected, but theoretical methods become numerically intractable. In this regime we find that the antiferromagnetic LRO persists to hole dopings of about 15%, providing a guideline for computational methods. Our results demonstrate that quantum gas microscopy of ultracold fermions in optical lattices can now address open questions on the low-temperature Hubbard model.The Hubbard Hamiltonian is a fundamental model for spinful lattice electrons describing a competition between kinetic energy t and interaction energy U [29]. In the limiting case of half-filling (average one particle per site) and dominant interactions (U/t 1) the Hubbard model maps to the Heisenberg model [1]. There, the exchange energy J = 4t 2 /U can give rise to antiferromagnetically ordered states at low temperatures [30]. This order persists for all finite U/t, where charge fluctuations reduce the ordering strength [31]. Away from half-filling, the coupling between motional and spin degrees of freedom is expected to give rise to a rich many-body phase diagram (see Fig. 1a), which is challenging to understand theoretically due to the fermion sign problem [32]. Even so, in the thermodynamic limit com...

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“…The LE of the TG gas is formally equivalent to the corresponding echo for a gas of noninteracting fermions [21]. The Loschmidt echo of one-dimensional interacting Bose gases was recently related [19] to a series of experiments [23][24][25] and theoretical studies [26][27][28][29][30][31] on interference between split parallel 1D Bose systems. …”

Section: Loschmidt Echo and Out-of-equilibrium Dynamics: Sudden Qmentioning

confidence: 99%

Pinning quantum phase transition in a Tonks-Girardeau gas: Diagnostics by ground-state fidelity and the Loschmidt echo

et al. 2012

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We study the pinning quantum phase transition in a Tonks-Girardeau gas, both in equilibrium and out of equilibrium, using the ground-state fidelity and the Loschmidt echo as diagnostic tools. The ground-state fidelity will have a dramatic decrease when the atomic density approaches the commensurate density of one particle per lattice well. This decrease is a signature of the pinning transition from the Tonks to the Mott insulating phase. We study the applicability of the fidelity for diagnosing the pinning transition in experimentally realistic scenarios. We find that fidelity can predict the particle number(s) at which the pinning occurs. In addition, we explore the out-of-equilibrium dynamics of the gas following a sudden quench with a lattice potential. We find that all properties of the ground-state fidelity are reflected in the Loschmidt echo dynamics, i.e., in the nonequilibrium dynamics of the Tonks-Girardeau gas initiated by a sudden quench of the lattice potential

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Probing quantum and thermal noise in an interacting many-body system

Cited by 243 publications

References 55 publications

Non-equilibrium dynamics of an unstable quantum pendulum explored in a spin-1 Bose–Einstein condensate

Non-equilibrium dynamics of an unstable quantum pendulum explored in a spin-1 Bose–Einstein condensate

A cold-atom Fermi–Hubbard antiferromagnet

Pinning quantum phase transition in a Tonks-Girardeau gas: Diagnostics by ground-state fidelity and the Loschmidt echo

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