Multipartite Entangled Spatial Modes of Ultracold Atoms Generated and Controlled by Quantum Measurement

Abstract

We show that the effect of measurement backaction results in the generation of multiple many-body spatial modes of ultracold atoms trapped in an optical lattice, when scattered light is detected. The multipartite mode entanglement properties and their nontrivial spatial overlap can be varied by tuning the optical geometry in a single setup. This can be used to engineer quantum states and dynamics of matter fields. We provide examples of multimode generalizations of parametric down-conversion, Dicke, and other states; investigate the entanglement properties of such states; and show how they can be transformed into a class of generalized squeezed states. Furthermore, we propose how these modes can be used to detect and measure entanglement in quantum gases. DOI: 10.1103/PhysRevLett.114.113604 PACS numbers: 42.50.Ct, 03.67.Bg, 03.75.Gg, 42.50.Dv Recently, the field of quantum gases [1,2] has grown considerably, due to the suitability of atomic systems for quantum simulation of a wide array of systems with origins in other fields, such as condensed matter and particle physics. Such systems also have use in entanglement and quantum information processing (QIP) [3]. Control is achieved by light fields, and there has been recent interest in the regime when the light exhibits decidedly quantum properties, thus uniting quantum optics with many-body physics (see Refs. [4,5] for reviews). This fully quantum regime enables one to go beyond standard questions of ultracold gases trapped in fixed classical potentials, thus broadening the field even further.Measurement backaction, the evolution of a state due to observation, is one of the primary manifestations of quantum mechanics. It was exploited in the breakthrough cavity QED experiments [6], where atoms were used as probes of quantum states of light. Intriguing Fock and Schrödinger cat states were prepared in a single cavity using quantum nondemolition (QND) methods. However, scaling to a large number of cavities provides an extreme challenge.In contrast, we consider a case where the roles of light and matter are reversed: Ultracold atoms are trapped in an optical lattice, and light is used as a global QND probe. Thus, the lattice sites represent the storage of multiple quantum states of matter fields, and the number of illuminated sites can be tuned from few to thousands, enabling scaling. We show how the quantum nature of light manifest in the measurement backaction can be used to establish a rich mode structure of the matter fields, with nontrivial delocalization over many sites and entanglement properties. These modes can be used for quantum state engineering, including multimode generalizations of parametric down-conversion (PDC) and Dicke states. We focus on the mode entanglement properties of these states, which exhibit genuine multipartite mode entanglement [7,8], and contrary to the entanglement inherent to the symmetrization of indistinguishable particles, may be extracted for use in QIP. In contrast to setups with atomic ensembles, we consider optical lattic...

Engineering many-body dynamics with quantum light potentials and measurements

“…We note also that in general, as the regions are defined by the matter mode structure, which is in turn defined by the light-matter interaction coefficients J m0 ii , the regions considered here need not be spatially contiguous, and indeed, the modes can have a very non-trivial spatial overlap with each other [18]. In this sense, one can more generally consider the interaction strengths as being classed as inter-and intramode, rather than short-and long-range.…”

“…In previous works [18,19], we have discussed how the light measurement backaction from the photons leaked by a cavity can be used to selectively suppress atomic dynamics in the standard Bose-Hubbard model, through constraints on the dynamics imposed by the rate at which photons are detected. We now go beyond this, and incorporate the cavity light-induced dynamics into such methods, thus uniting the measurement backaction effect with the cavity backaction for the first time.…”

“…This set of states is defined by the matter mode structure, and hence depends on the modefunctions of the measurement cavity and pump [18]. The ensuing atomic dynamics must take place within this measurement subspace, thus undergoing quantum Zeno dynamics [37].…”

“…Uniting these fields [4,5] broadens both, and goes beyond the cases when either the light or matter are treated classically. Experimental [6][7][8][9][10][11] and theoretical works in this regime have revealed many interesting phenomena, such as the preparation of atomic states and dynamics [12][13][14][15][16][17][18][19], non-destructive measurement [20][21][22][23][24], many-body light-matter entanglement [23], self-organisation, and other new quantum phases [25][26][27][28][29][30][31][32][33][34][35][36].…”

Zeno Hall Effect

“…1 (a)) [23][24][25]; (ii) the noncommutativity of position operators in a constrained Bloch band with a nontrivial Berry curvature [26]. (i) exploits the quantum Zeno (QZ) effect [27][28][29], which is well studied in the context of quantum measurement [30,31] and occurs also for strong dissipation [32-34] as a continuous limit of repeated measurements [23]. (ii) shares the same physics behind the anomalous Hall effect [35].…”