arXiv subjects

Aaron Z. Goldberg

Publications and source records attributed to Aaron Z. Goldberg.

48 records · Page 3Linked to original sources

arXiv2020

Transcoherent states: Optical states for maximal generation of atomic coherence

Quantum technologies are built on the power of coherent superposition. Atomic coherence is typically generated from optical coherence, most often via Rabi oscillations. However, canonical coherent states of light create imperfect resources; a fully-quantized description of "$\tfracπ{2}$ pulses" shows that the atomic superpositions generated remain entangled with the light. We show that there are quantum states of light that generate coherent atomic states perfectly, with no residual atom-field entanglement. These states can be found for arbitrarily short times and approach slightly-number-squeezed $\tfracπ{2}$ pulses in the limit of large intensities; similar ideal states can be found for any $(2k+1)\tfracπ{2}$ pulses, requiring more number squeezing with increasing $k$. Moreover, these states can be repeatedly used as "quantum catalysts" to successfully generate coherent atomic states with high probability. From this perspective we have identified states that are "more coherent" than coherent states.

quant-ph↗

arXiv2020

Nonclassical states that generate zero entanglement with a beam splitter

Beam splitters are routinely used for generating entanglement. Their entangling properties have been studied extensively, with nonclassicality of the input states a prerequisite for entanglement at the output. Here we quantify the amount of entanglement generated by weakly-reflecting beam splitters, and look for nonclassical states that are not entangled by general beam splitters. We find that inputting highly nonclassical combinations of unpolarized states that are squeezed and displaced onto a beam splitter can still yield separable output states. This result is crucial for understanding the generation of modal entanglement by beam splitters.

quant-ph↗

arXiv2020

Multiphase estimation without a reference mode

Multiphase estimation is a paradigmatic example of a multiparameter problem. When measuring multiple phases embedded in interferometric networks, specially-tailored input quantum states achieve enhanced sensitivities compared with both single-parameter and classical estimation schemes. Significant attention has been devoted to defining the optimal strategies for the scenario in which all of the phases are evaluated with respect to a common reference mode, in terms of optimal probe states and optimal measurement operators. As well, the strategies assume unlimited external resources, which is experimentally unrealistic. Here, we optimize a generalized scenario that treats all of the phases on an equal footing and takes into account the resources provided by external references. We show that the absence of an external reference mode reduces the number of simultaneously estimatable parameters, owing to the immeasurability of global phases, and that the symmetries of the parameters being estimated dictate the symmetries of the optimal probe states. Finally, we provide insight for constructing optimal measurements in this generalized scenario. The experimental viability of this work underlies its immediate practical importance beyond fundamental physics.

quant-ph↗

arXiv2020

Quantum theory of polarimetry: From quantum operations to Mueller matrices

Quantum descriptions of polarization show the rich degrees of freedom underlying classical light. While changes in polarization of light are well-described classically, a full quantum description of polarimetry, which characterizes substances by their effects on incident light's polarization, is lacking. We provide sets of quantum channels that underlie classical polarimetry and thus correspond to arbitrary Mueller matrices. This allows us to inspect how the quantum properties of light change in a classical polarimetry experiment, and to investigate the extra flexibility that quantum states have during such transformations. Moreover, our quantum channels imply a new method for discriminating between depolarizing and nondepolarizing Mueller matrices, which has been the subject of much research. This theory can now be taken advantage of to improve estimation strategies in classical polarimetry and to further explore the boundaries between classical and quantum polarization.

quant-ph↗

arXiv2020

Operational symmetries of entangled states

Quantum entanglement obscures the notion of local operations; there exist quantum states for which all local actions on one subsystem can be equivalently realized by actions on another. We characterize the states for which this fundamental property of entanglement does and does not hold, including multipartite and mixed states. Our results lead to a method for quantifying entanglement based on operational symmetries and has connections to quantum steering, envariance, the Reeh-Schlieder theorem, and classical entanglement.

quant-ph↗

arXiv2019

Emergence of singularities from decoherence: Quantum catastrophes

We use a master equation to study the dynamics of two coupled macroscopic quantum systems (e.g.\ a Josephson junction made of two Bose-Einstein condensates or two spin states of an ensemble of trapped ions) subject to a weak continuous measurement. If the coupling between the two systems is suddenly switched on the resulting dynamics leads to caustics (fold and cusp catastrophes) in the number-difference probability distribution, and at the same time the measurement gradually induces a quantum-to-classical transition. Decoherence is often invoked to help resolve paradoxes associated with macroscopic quantum mechanics, but here, on the contrary, caustics are well-behaved in the quantum (many-particle) theory and divergent in the classical (mean-field) theory. Caustics thus represent a breakdown of the classical theory towards which decoherence seems to inevitably lead. We find that measurement backaction plays a crucial role in softening the resulting singularities and calculate the modification to the Arnol'd index which governs the scaling of the caustic's amplitude with the number of atoms. The Arnol'd index acts as a critical exponent for the formation of singularities during quantum dynamics and its modification by the open nature of the system is analogous to the modification of the critical exponents of phase transitions occurring in open systems.

cond-mat.quant-gas↗

arXiv2019

Entanglement generation via diffraction

Quantum entanglement is an important resource for next-generation technologies. We show that diffracting systems can supplant beam splitters, and more generally interferometric networks, for entanglement generation -- systems as simple as screens with pinholes can create entanglement. We then discuss the necessary and sufficient conditions for entanglement to be generated by states input to any passive linear interferometric network. Entanglement generated in free space can now be harnessed in quantum-optical applications ranging from quantum computation and communication to quantum metrology.

quant-ph↗

arXiv2019

Quantum-limited Euler angle measurements using anticoherent states

Many protocols require precise rotation measurement. Here we present a general class of states that surpass the shot noise limit for measuring rotation around arbitrary axes. We then derive a quantum Cramér-Rao bound for simultaneously estimating all three parameters of a rotation (e.g., the Euler angles), and discuss states that achieve Heisenberg-limited sensitivities for all parameters; the bound is saturated by "anticoherent" states [Zimba, Electron. J. Theor. Phys. 3, 143 (2006)] (we are reluctant to use "anticoherent" to describe the states, but the name has become commonplace over the last decade). Anticoherent states have garnered much attention in recent years, and we elucidate a geometrical technique for finding new examples of such states. Finally, we discuss the potential for divergences in multiparameter estimation due to singularities in spherical coordinate systems. Our results are useful for a variety of quantum metrology and quantum communication applications.

quant-ph↗

arXiv2019

Perturbative expansion of entanglement negativity using patterned matrix calculus

Negativity is an entanglement monotone frequently used to quantify entanglement in bipartite states. Because negativity is a non-analytic function of a density matrix, existing methods used in the physics literature are insufficient to compute its derivatives. To this end we develop techniques in the calculus of complex, patterned matrices and use them to conduct a perturbative analysis of negativity in terms of arbitrary variations of the density operator. The result is an easy-to-implement expansion that can be carried out to all orders. On the way we provide convenient representations of the partial transposition map appearing in the definition of negativity. Our methods are well-suited to study the growth and decay of entanglement in a wide range of physical systems, including the generic linear growth of entanglement in many-body systems, and have broad relevance to many functions of quantum states and observables.

quant-ph↗

arXiv2018

Perfect polarization for arbitrary light beams

Polarization of light is harnessed in an abundance of classical and quantum applications. Characterizing polarization in a classical sense is done resoundingly successfully using the Stokes parameters, and numerous proposals offer new quantum counterparts of this characterization. The latter often rely on distance measures from completely polarized or unpolarized light. We here show that the accepted class of perfectly polarized quantum states of light is severely lacking in terms of both pure states and mixed states. By appealing to symmetry and geometry arguments we determine all of the states corresponding to perfect polarization, and show that the accepted class of completely polarized quantum states is only a subset of our result. We use this result to reinterpret the canonical degree of polarization, commenting on its interpretation for classical and quantum light. Our results are necessary for any further characterizations of light's polarization.

quant-ph↗

arXiv2018

Simulating one-dimensional systems with stationary Rydberg dark polaritons

Electromagnetically-induced transparency (EIT) with Rydberg atoms enables strong interactions between atoms to be controlled and measured by pulses of light. Consequently, Rydberg dark polaritons are a promising platform for quantum simulations. Of particular interest are simulations of one-dimensional systems, known to exhibit unique properties compared to their higher-dimensional counterparts. One limitation of standard EIT is that reducing the polariton group velocity to bring the dark polaritons to rest also implies activating strong Rydberg interactions. To achieve independent control of polariton speed and interaction strength, we propose a stationary light-scheme to bring Rydberg polaritons to a stand-still. This allows them to remain primarily photonic and, therefore, non-interacting, before Rydberg interactions are turned on. Once activated, in the dilute regime and in the presence of strong transverse confinement, the strong polarizabilities of Rydberg atoms give rise to an effective contact interaction between polaritons. By tuning the various parameters of the stationary-light scheme, the effective one-dimensional scattering length may be adjusted to yield various kinds of physics, including the regime of a Tonks-Girardeau gas, when polaritons exhibit fermionic behavior. We outline a protocol to observe the resulting spatial correlations between neighboring polaritons.

quant-ph↗

arXiv2016

Chondrule Transport in Protoplanetary Disks

Chondrule formation remains one of the most elusive early Solar System events. Here, we take the novel approach of employing numerical simulations to investigate chondrule origin beyond purely cosmochemical methods. We model the transport of generically-produced chondrules and dust in a 1D viscous protoplanetary disk model, in order to constrain the chondrule formation events. For a single formation event we are able to match analytical predictions of the memory chondrule and dust populations retain of each other (complementarity), finding that a large mass accretion rate ($\gtrsim 10^{-7}$~M$_\odot$~yr$^{-1}$) allows for delays on the order of the disk's viscous timescale between chondrule formation and chondrite accretion. Further, we find older disks to be severely diminished of chondrules, with accretion rates $\lesssim 10^{-9}$~M$_\odot$~yr$^{-1}$ for nominal parameters. We then characterize the distribution of chondrule origins in both space and time, as functions of disk parameters and chondrule formation rates, in runs with continuous chondrule formation and both static and evolving disks. Our data suggest that these can account for the observed diversity between distinct chondrite classes, if some diversity in accretion time is allowed for.

astro-ph.EP↗