Quantum optics theoryhttp://hdl.handle.net/2117/238582020-01-25T12:26:17Z2020-01-25T12:26:17ZSymphony on strong field approximationAmini, KasraBiegert, JensCalegari, FrancescaChacón, AlexisCiappina, Marcelo F.Dauphin, AlexandreEfimov, Dmitry K.Faria, Carla Figueira de MorissonGiergiel, KrzysztofGniewek, PiotrLandsman, Alexandra S.Lesiuk, MichałMandrysz, MichałMaxwell, Andrew S.Moszynski, RobertOrtmann, LisaPérez-Hernández, Jose AntonioPicón, AntonioPisanty, EmilioPrauzner-Bechcicki, JakubSacha, KrzysztofSuárez, NoslenZaïr, AmelleZakrzewski, JakubLewenstein, Maciejhttp://hdl.handle.net/2117/1709992019-10-29T06:56:25Z2019-10-28T17:00:31ZSymphony on strong field approximation
Amini, Kasra; Biegert, Jens; Calegari, Francesca; Chacón, Alexis; Ciappina, Marcelo F.; Dauphin, Alexandre; Efimov, Dmitry K.; Faria, Carla Figueira de Morisson; Giergiel, Krzysztof; Gniewek, Piotr; Landsman, Alexandra S.; Lesiuk, Michał; Mandrysz, Michał; Maxwell, Andrew S.; Moszynski, Robert; Ortmann, Lisa; Pérez-Hernández, Jose Antonio; Picón, Antonio; Pisanty, Emilio; Prauzner-Bechcicki, Jakub; Sacha, Krzysztof; Suárez, Noslen; Zaïr, Amelle; Zakrzewski, Jakub; Lewenstein, Maciej
This paper has been prepared by the Symphony collaboration (University of Warsaw,
Uniwersytet Jagielloński, DESY/CNR and ICFO) on the occasion of the 25th anniversary of
the ‘simple man’s models’ which underlie most of the phenomena that occur when intense
ultrashort laser pulses interact with matter. The phenomena in question include high-harmonic
generation (HHG), above-threshold ionization (ATI), and non-sequential multielectron
ionization (NSMI). ‘Simple man’s models’ provide both an intuitive basis for understanding
the numerical solutions of the time-dependent Schrödinger equation and the motivation for the
powerful analytic approximations generally known as the strong field approximation (SFA).
In this paper we first review the SFA in the form developed by us in the last 25 years. In this approach the SFA is a method to solve the TDSE, in which the non-perturbative interactions
are described by including continuum–continuum interactions in a systematic perturbation-like
theory. In this review we focus on recent applications of the SFA to HHG, ATI and NSMI from
multi-electron atoms and from multi-atom molecules. The main novel part of the presented
theory concerns generalizations of the SFA to: (i) time-dependent treatment of two-electron
atoms, allowing for studies of an interplay between electron impact ionization and resonant
excitation with subsequent ionization; (ii) time-dependent treatment in the single active
electron approximation of ‘large’ molecules and targets which are themselves undergoing
dynamics during the HHG or ATI processes. In particular, we formulate the general expressions
for the case of arbitrary molecules, combining input from quantum chemistry and quantum
dynamics. We formulate also theory of time-dependent separable molecular potentials to model
analytically the dynamics of realistic electronic wave packets for molecules in strong laser
fields.
2019-10-28T17:00:31ZAmini, KasraBiegert, JensCalegari, FrancescaChacón, AlexisCiappina, Marcelo F.Dauphin, AlexandreEfimov, Dmitry K.Faria, Carla Figueira de MorissonGiergiel, KrzysztofGniewek, PiotrLandsman, Alexandra S.Lesiuk, MichałMandrysz, MichałMaxwell, Andrew S.Moszynski, RobertOrtmann, LisaPérez-Hernández, Jose AntonioPicón, AntonioPisanty, EmilioPrauzner-Bechcicki, JakubSacha, KrzysztofSuárez, NoslenZaïr, AmelleZakrzewski, JakubLewenstein, MaciejThis paper has been prepared by the Symphony collaboration (University of Warsaw,
Uniwersytet Jagielloński, DESY/CNR and ICFO) on the occasion of the 25th anniversary of
the ‘simple man’s models’ which underlie most of the phenomena that occur when intense
ultrashort laser pulses interact with matter. The phenomena in question include high-harmonic
generation (HHG), above-threshold ionization (ATI), and non-sequential multielectron
ionization (NSMI). ‘Simple man’s models’ provide both an intuitive basis for understanding
the numerical solutions of the time-dependent Schrödinger equation and the motivation for the
powerful analytic approximations generally known as the strong field approximation (SFA).
In this paper we first review the SFA in the form developed by us in the last 25 years. In this approach the SFA is a method to solve the TDSE, in which the non-perturbative interactions
are described by including continuum–continuum interactions in a systematic perturbation-like
theory. In this review we focus on recent applications of the SFA to HHG, ATI and NSMI from
multi-electron atoms and from multi-atom molecules. The main novel part of the presented
theory concerns generalizations of the SFA to: (i) time-dependent treatment of two-electron
atoms, allowing for studies of an interplay between electron impact ionization and resonant
excitation with subsequent ionization; (ii) time-dependent treatment in the single active
electron approximation of ‘large’ molecules and targets which are themselves undergoing
dynamics during the HHG or ATI processes. In particular, we formulate the general expressions
for the case of arbitrary molecules, combining input from quantum chemistry and quantum
dynamics. We formulate also theory of time-dependent separable molecular potentials to model
analytically the dynamics of realistic electronic wave packets for molecules in strong laser
fields.Knotting fractional-order knots with the polarization state of lightPisanty, EmilioMachado, Gerard J.Vicuña-Hernández, VerónicaPicón, AntonioCeli, AlessioPérez Torres, JuanLewenstein, Maciejhttp://hdl.handle.net/2117/1668612019-12-19T05:37:00Z2019-07-25T10:32:01ZKnotting fractional-order knots with the polarization state of light
Pisanty, Emilio; Machado, Gerard J.; Vicuña-Hernández, Verónica; Picón, Antonio; Celi, Alessio; Pérez Torres, Juan; Lewenstein, Maciej
The fundamental polarization singularities of monochromatic light are normally associated with invariance under coordinated rotations: symmetry operations that rotate the spatial dependence of an electromagnetic field by an angle and its polarization by a multiple of that angle. These symmetries are generated by mixed angular momenta of the form J_γ = L + γ S, and they generally induce Möbius-strip topologies, with the coordination parameter restricted to integer and half-integer values. In this work we construct beams of light that are invariant under coordinated rotations for arbitrary rational γ, by exploiting the higher internal symmetry of ‘bicircular’ superpositions of counter-rotating circularly polarized beams at different frequencies. We show that these beams have the topology of a torus knot, which reflects the subgroup generated by the torus-knot angular momentum J_γ, and we characterize the resulting optical polarization singularity using third-and higher-order field moment tensors, which we experimentally observe using nonlinear polarization tomography.
2019-07-25T10:32:01ZPisanty, EmilioMachado, Gerard J.Vicuña-Hernández, VerónicaPicón, AntonioCeli, AlessioPérez Torres, JuanLewenstein, MaciejThe fundamental polarization singularities of monochromatic light are normally associated with invariance under coordinated rotations: symmetry operations that rotate the spatial dependence of an electromagnetic field by an angle and its polarization by a multiple of that angle. These symmetries are generated by mixed angular momenta of the form J_γ = L + γ S, and they generally induce Möbius-strip topologies, with the coordination parameter restricted to integer and half-integer values. In this work we construct beams of light that are invariant under coordinated rotations for arbitrary rational γ, by exploiting the higher internal symmetry of ‘bicircular’ superpositions of counter-rotating circularly polarized beams at different frequencies. We show that these beams have the topology of a torus knot, which reflects the subgroup generated by the torus-knot angular momentum J_γ, and we characterize the resulting optical polarization singularity using third-and higher-order field moment tensors, which we experimentally observe using nonlinear polarization tomography.Terahertz field control of in-plane orbital order in La0.5Sr1.5MnO4Miller, Timothy A.Chhajlany, Ravindra W.Tagliacozzo, LucaGreen, BertramKovalev, SergeyPrabhakaran, DharmalingamLewenstein, MaciejGensch, MichaelWall, Simonhttp://hdl.handle.net/2117/791402019-04-30T15:08:36Z2015-11-12T14:43:09ZTerahertz field control of in-plane orbital order in La0.5Sr1.5MnO4
Miller, Timothy A.; Chhajlany, Ravindra W.; Tagliacozzo, Luca; Green, Bertram; Kovalev, Sergey; Prabhakaran, Dharmalingam; Lewenstein, Maciej; Gensch, Michael; Wall, Simon
In-plane anisotropic ground states are ubiquitous in correlated solids such as pnictides, cuprates and manganites. They can arise from doping Mott insulators and compete with phases such as superconductivity; however, their origins are debated. Strong coupling between lattice, charge, orbital and spin degrees of freedom results in simultaneous ordering of multiple parameters, masking the mechanism that drives the transition. Here we demonstrate that the orbital domains in a manganite can be oriented by the polarization of a pulsed THz light field. Through the application of a Hubbard model, we show that domain control can be achieved by enhancing the local Coulomb interactions, which drive domain reorientation. Our results highlight the key role played by the Coulomb interaction in the control and manipulation of orbital order in the manganites and demonstrate a new way to use THz to understand and manipulate anisotropic phases in a potentially broad range of correlated materials.
2015-11-12T14:43:09ZMiller, Timothy A.Chhajlany, Ravindra W.Tagliacozzo, LucaGreen, BertramKovalev, SergeyPrabhakaran, DharmalingamLewenstein, MaciejGensch, MichaelWall, SimonIn-plane anisotropic ground states are ubiquitous in correlated solids such as pnictides, cuprates and manganites. They can arise from doping Mott insulators and compete with phases such as superconductivity; however, their origins are debated. Strong coupling between lattice, charge, orbital and spin degrees of freedom results in simultaneous ordering of multiple parameters, masking the mechanism that drives the transition. Here we demonstrate that the orbital domains in a manganite can be oriented by the polarization of a pulsed THz light field. Through the application of a Hubbard model, we show that domain control can be achieved by enhancing the local Coulomb interactions, which drive domain reorientation. Our results highlight the key role played by the Coulomb interaction in the control and manipulation of orbital order in the manganites and demonstrate a new way to use THz to understand and manipulate anisotropic phases in a potentially broad range of correlated materials.Inequivalence of entanglement, steering, and Bell nonlocality for general measurementsQuintino, Marco TulioVértesi, TamasCavalcanti, DanielAugusiak, RemigiuszDemianowicz, MaciejAcín, AntonioBrunner, Nicolashttp://hdl.handle.net/2117/790102019-01-24T10:27:20Z2015-11-11T12:06:43ZInequivalence of entanglement, steering, and Bell nonlocality for general measurements
Quintino, Marco Tulio; Vértesi, Tamas; Cavalcanti, Daniel; Augusiak, Remigiusz; Demianowicz, Maciej; Acín, Antonio; Brunner, Nicolas
Einstein-Podolsky-Rosen steering is a form of inseparability in quantum theory commonly acknowledged to be intermediate between entanglement and Bell nonlocality. However, this statement has so far only been proven for a restricted class of measurements, namely, projective measurements. Here we prove that entanglement, one-way steering, two-way steering, and nonlocality are genuinely different considering general measurements, i.e., single round positive-operator-valued measures. Finally, we show that the use of sequences of measurements is relevant for steering tests, as they can be used to reveal “hidden steering.”
2015-11-11T12:06:43ZQuintino, Marco TulioVértesi, TamasCavalcanti, DanielAugusiak, RemigiuszDemianowicz, MaciejAcín, AntonioBrunner, NicolasEinstein-Podolsky-Rosen steering is a form of inseparability in quantum theory commonly acknowledged to be intermediate between entanglement and Bell nonlocality. However, this statement has so far only been proven for a restricted class of measurements, namely, projective measurements. Here we prove that entanglement, one-way steering, two-way steering, and nonlocality are genuinely different considering general measurements, i.e., single round positive-operator-valued measures. Finally, we show that the use of sequences of measurements is relevant for steering tests, as they can be used to reveal “hidden steering.”Nonlocality in many-body quantum systems detected with two-body correlatorsTura, J.Augusiak, RemigiuszSainz, A. B.Lücke, B.Klempt, C.Lewenstein, MaciejAcin, Antoniohttp://hdl.handle.net/2117/789582019-01-24T10:19:06Z2015-11-10T12:19:08ZNonlocality in many-body quantum systems detected with two-body correlators
Tura, J.; Augusiak, Remigiusz; Sainz, A. B.; Lücke, B.; Klempt, C.; Lewenstein, Maciej; Acin, Antonio
Contemporary understanding of correlations in quantum many-body systems and in quantum phase transitions
is based to a large extent on the recent intensive studies of entanglement in many-body systems. In contrast,
much less is known about the role of quantum nonlocality in these systems, mostly because the available
multipartite Bell inequalities involve high-order correlations among many particles, which are hard to access
theoretically, and even harder experimentally. Standard, ”theorist- and experimentalist-friendly” many-body
observables involve correlations among only few (one, two, rarely three...) particles. Typically, there is no
multipartite Bell inequality for this scenario based on such low-order correlations. Recently, however, we have
succeeded in constructing multipartite Bell inequalities that involve two- and one-body correlations only, and
showed how they revealed the nonlocality in many-body systems relevant for nuclear and atomic physics [Science
344, 1256 (2014)]. With the present contribution we continue our work on this problem. On the one hand,
we present a detailed derivation of the above Bell inequalities, pertaining to permutation symmetry among the
involved parties. On the other hand, we present a couple of new results concerning such Bell inequalities. First,
we characterize their tightness. We then discuss maximal quantum violations of these inequalities in the general
case, and their scaling with the number of parties. Moreover, we provide new classes of two-body Bell inequalities
which reveal nonlocality of the Dicke states—ground states of physically relevant and experimentally
realizable Hamiltonians. Finally, we shortly discuss various scenarios for nonlocality detection in mesoscopic
systems of trapped ions or atoms, and by atoms trapped in the vicinity of designed nanostructures.
2015-11-10T12:19:08ZTura, J.Augusiak, RemigiuszSainz, A. B.Lücke, B.Klempt, C.Lewenstein, MaciejAcin, AntonioContemporary understanding of correlations in quantum many-body systems and in quantum phase transitions
is based to a large extent on the recent intensive studies of entanglement in many-body systems. In contrast,
much less is known about the role of quantum nonlocality in these systems, mostly because the available
multipartite Bell inequalities involve high-order correlations among many particles, which are hard to access
theoretically, and even harder experimentally. Standard, ”theorist- and experimentalist-friendly” many-body
observables involve correlations among only few (one, two, rarely three...) particles. Typically, there is no
multipartite Bell inequality for this scenario based on such low-order correlations. Recently, however, we have
succeeded in constructing multipartite Bell inequalities that involve two- and one-body correlations only, and
showed how they revealed the nonlocality in many-body systems relevant for nuclear and atomic physics [Science
344, 1256 (2014)]. With the present contribution we continue our work on this problem. On the one hand,
we present a detailed derivation of the above Bell inequalities, pertaining to permutation symmetry among the
involved parties. On the other hand, we present a couple of new results concerning such Bell inequalities. First,
we characterize their tightness. We then discuss maximal quantum violations of these inequalities in the general
case, and their scaling with the number of parties. Moreover, we provide new classes of two-body Bell inequalities
which reveal nonlocality of the Dicke states—ground states of physically relevant and experimentally
realizable Hamiltonians. Finally, we shortly discuss various scenarios for nonlocality detection in mesoscopic
systems of trapped ions or atoms, and by atoms trapped in the vicinity of designed nanostructures.Quench dynamics of dipolar fermions in a one-dimensional harmonic trapGraß, Tobiashttp://hdl.handle.net/2117/789432019-01-24T10:20:14Z2015-11-09T16:32:24ZQuench dynamics of dipolar fermions in a one-dimensional harmonic trap
Graß, Tobias
We study a system of few fermions in a one-dimensional harmonic trap and focus on the case of dipolar
majority particles in contact with a single impurity. The impurity is used both for quenching the system and
for tracking the system evolution after the quench. Employing exact diagonalization, we investigate relaxation
and thermalization properties. In the absence of dipolar interactions, the system dynamics remains oscillatory
even on long time scales. On the other hand, repulsive as well as attractive dipolar interactions lead to quick
relaxation to the diagonal ensemble average, which is significantly different from corresponding thermal averages.
A Wigner-shaped level spacing distribution indicates level repulsion and thus chaotic dynamical behavior due to
the presence of dipolar interactions.
2015-11-09T16:32:24ZGraß, TobiasWe study a system of few fermions in a one-dimensional harmonic trap and focus on the case of dipolar
majority particles in contact with a single impurity. The impurity is used both for quenching the system and
for tracking the system evolution after the quench. Employing exact diagonalization, we investigate relaxation
and thermalization properties. In the absence of dipolar interactions, the system dynamics remains oscillatory
even on long time scales. On the other hand, repulsive as well as attractive dipolar interactions lead to quick
relaxation to the diagonal ensemble average, which is significantly different from corresponding thermal averages.
A Wigner-shaped level spacing distribution indicates level repulsion and thus chaotic dynamical behavior due to
the presence of dipolar interactions.Locality of temperature in spin chainsHernández-Santana, SenaidaRiera, ArnauHovhannisyan, Karen V.Perarnau-Llobet, MartíTagliacozzo, Lucahttp://hdl.handle.net/2117/789292019-01-24T10:19:23Z2015-11-09T09:02:29ZLocality of temperature in spin chains
Hernández-Santana, Senaida; Riera, Arnau; Hovhannisyan, Karen V.; Perarnau-Llobet, Martí; Tagliacozzo, Luca
In traditional thermodynamics, temperature is a local quantity: a subsystem of a large thermal system is in a thermal state at the same temperature as the original system. For strongly interacting systems, however, the locality of temperature breaks down. We study the possibility of associating an effective thermal state to subsystems of infinite chains of interacting spin particles of arbitrary finite dimension. We study the effect of correlations and criticality in the definition of this effective thermal state and discuss the possible implications for the classical simulation of thermal quantum systems.
2015-11-09T09:02:29ZHernández-Santana, SenaidaRiera, ArnauHovhannisyan, Karen V.Perarnau-Llobet, MartíTagliacozzo, LucaIn traditional thermodynamics, temperature is a local quantity: a subsystem of a large thermal system is in a thermal state at the same temperature as the original system. For strongly interacting systems, however, the locality of temperature breaks down. We study the possibility of associating an effective thermal state to subsystems of infinite chains of interacting spin particles of arbitrary finite dimension. We study the effect of correlations and criticality in the definition of this effective thermal state and discuss the possible implications for the classical simulation of thermal quantum systems.Progress towards a unified approach to entanglement distributionStreltsov, AlexanderAugusiak, RemigiuszDemianowicz, MaciejLewenstein, Maciejhttp://hdl.handle.net/2117/789042019-01-24T10:20:27Z2015-11-06T13:45:54ZProgress towards a unified approach to entanglement distribution
Streltsov, Alexander; Augusiak, Remigiusz; Demianowicz, Maciej; Lewenstein, Maciej
Entanglement distribution is key to the success of secure communication schemes based on quantum mechanics, and there is a strong need for an ultimate architecture able to overcome the limitations of recent proposals such as those based on entanglement percolation or quantum repeaters. In this work we provide a broad theoretical background for the development of such technologies. In particular, we investigate the question of whether entanglement distribution is more efficient if some amount of entanglement—or some amount of correlations in general—is available prior to the transmission stage of the protocol. We show that in the presence of noise the answer to this question strongly depends on the type of noise and on the way the entanglement is quantified. On the one hand, subadditive entanglement measures do not show an advantage of preshared correlations if entanglement is established via combinations of single-qubit Pauli channels. On the other hand, based on the superadditivity conjecture of distillable entanglement, we provide evidence that this phenomenon occurs for this measure. These results strongly suggest that sending one half of some pure entangled state down a noisy channel is the best strategy for any subadditive entanglement quantifier, thus paving the way to a unified approach for entanglement distribution which does not depend on the nature of noise. We also provide general bounds for entanglement distribution involving quantum discord and present a counterintuitive phenomenon of the advantage of arbitrarily little entangled states over maximally entangled ones, which may also occur for quantum channels relevant in experiments.
2015-11-06T13:45:54ZStreltsov, AlexanderAugusiak, RemigiuszDemianowicz, MaciejLewenstein, MaciejEntanglement distribution is key to the success of secure communication schemes based on quantum mechanics, and there is a strong need for an ultimate architecture able to overcome the limitations of recent proposals such as those based on entanglement percolation or quantum repeaters. In this work we provide a broad theoretical background for the development of such technologies. In particular, we investigate the question of whether entanglement distribution is more efficient if some amount of entanglement—or some amount of correlations in general—is available prior to the transmission stage of the protocol. We show that in the presence of noise the answer to this question strongly depends on the type of noise and on the way the entanglement is quantified. On the one hand, subadditive entanglement measures do not show an advantage of preshared correlations if entanglement is established via combinations of single-qubit Pauli channels. On the other hand, based on the superadditivity conjecture of distillable entanglement, we provide evidence that this phenomenon occurs for this measure. These results strongly suggest that sending one half of some pure entangled state down a noisy channel is the best strategy for any subadditive entanglement quantifier, thus paving the way to a unified approach for entanglement distribution which does not depend on the nature of noise. We also provide general bounds for entanglement distribution involving quantum discord and present a counterintuitive phenomenon of the advantage of arbitrarily little entangled states over maximally entangled ones, which may also occur for quantum channels relevant in experiments.Energetics and Control of Ultracold Isotope-Exchange Reactions between Heteronuclear Dimers in External FieldsTomza, Michałhttp://hdl.handle.net/2117/788912019-01-24T10:25:00Z2015-11-06T12:22:49ZEnergetics and Control of Ultracold Isotope-Exchange Reactions between Heteronuclear Dimers in External Fields
Tomza, Michał
We show that isotope-exchange reactions between ground-state alkali-metal, alkaline-earth-metal, and lanthanide heteronuclear dimers consisting of two isotopes of the same atom are exothermic with an energy change in the range of 1–8000 MHz, thus resulting in cold or ultracold products. For these chemical reactions, there are only one rovibrational and at most several hyperfine possible product states. The number and energetics of open and closed reactive channels can be controlled by the laser and magnetic fields. We suggest a laser-induced isotope- and state-selective Stark shift control to tune the exothermic isotope-exchange reactions to become endothermic, thus providing the ground for testing models of the chemical reactivity. The present proposal opens the way for studying the state-to-state dynamics of ultracold chemical reactions beyond the universal limit with a meaningful control over the quantum states of both reactants and products.
2015-11-06T12:22:49ZTomza, MichałWe show that isotope-exchange reactions between ground-state alkali-metal, alkaline-earth-metal, and lanthanide heteronuclear dimers consisting of two isotopes of the same atom are exothermic with an energy change in the range of 1–8000 MHz, thus resulting in cold or ultracold products. For these chemical reactions, there are only one rovibrational and at most several hyperfine possible product states. The number and energetics of open and closed reactive channels can be controlled by the laser and magnetic fields. We suggest a laser-induced isotope- and state-selective Stark shift control to tune the exothermic isotope-exchange reactions to become endothermic, thus providing the ground for testing models of the chemical reactivity. The present proposal opens the way for studying the state-to-state dynamics of ultracold chemical reactions beyond the universal limit with a meaningful control over the quantum states of both reactants and products.Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potentialLevinsen, JesperMassignan, PietroBruun, Georg M.Parish, Meera M.http://hdl.handle.net/2117/788462019-01-24T10:28:52Z2015-11-05T16:33:13ZStrong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential
Levinsen, Jesper; Massignan, Pietro; Bruun, Georg M.; Parish, Meera M.
A major challenge in modern physics is to accurately describe strongly interacting quantum many-body systems. One-dimensional systems provide fundamental insights because they are often amenable to exact methods. However, no exact solution is known for the experimentally relevant case of external confinement. We propose a powerful ansatz for the one-dimensional Fermi gas in a harmonic potential near the limit of infinite short-range repulsion. For the case of a single impurity in a Fermi sea, we show that our ansatz is indistinguishable from numerically exact results in both the few- and many-body limits. We furthermore derive an effective Heisenberg spin-chain model corresponding to our ansatz, valid for any spin-mixture, within which we obtain the impurity eigenstates analytically. In particular, the classical Pascal’s triangle emerges in the expression for the ground-state wave function. As well as providing an important benchmark for strongly correlated physics, our results are relevant for emerging quantum technologies, where a precise knowledge of one-dimensional quantum states is paramount.
2015-11-05T16:33:13ZLevinsen, JesperMassignan, PietroBruun, Georg M.Parish, Meera M.A major challenge in modern physics is to accurately describe strongly interacting quantum many-body systems. One-dimensional systems provide fundamental insights because they are often amenable to exact methods. However, no exact solution is known for the experimentally relevant case of external confinement. We propose a powerful ansatz for the one-dimensional Fermi gas in a harmonic potential near the limit of infinite short-range repulsion. For the case of a single impurity in a Fermi sea, we show that our ansatz is indistinguishable from numerically exact results in both the few- and many-body limits. We furthermore derive an effective Heisenberg spin-chain model corresponding to our ansatz, valid for any spin-mixture, within which we obtain the impurity eigenstates analytically. In particular, the classical Pascal’s triangle emerges in the expression for the ground-state wave function. As well as providing an important benchmark for strongly correlated physics, our results are relevant for emerging quantum technologies, where a precise knowledge of one-dimensional quantum states is paramount.