Ion-atom physics Carlo Sias Istituto Nazionale di Ricerca Metrologica - INRIM European Laboratory for Nonlinear Spectroscopy - LENS Gressoney, 13 September 2018 Roots.. Understanding physics enables new technology Thermodynamics Optics, spectroscopy ..and future Were are we with quantum mechanics? Neutral atoms Ions Photons Squids Quantum dots ... and many others ..at a good point! ..and future Were are we with quantum mechanics? Neutral atoms Ions Photons Squids Quantum dots ... and many others ..at a good point! ..and future Were are we with quantum mechanics? Neutral atoms Ions Photons Can we think of a composite system formed by two Squids Quantum dots coupled quantum systems? ... and many others ..at a good point! Ultracold atoms - overview Same fields, different approaches Coherent matter Single particles Ultracold atoms - overview Same fields, different approaches Coherent matter Single particles Many-body physics Blatt, Roos Nat. Phys. 2012 Ultracold atoms - overview Same fields, different approaches Coherent matter Single particles Many-body physics Blatt, Roos Nat. Phys. 2012 Single particle manipulation Greiner group Blatt group Ultracold atoms - overview Same fields, different approaches CLOCKS! Coherent matter Single particles Many-body physics Blatt, Roos Nat. Phys. 2012 Single particle manipulation Greiner group Blatt group Hybrid quantum systems Quantum degenerate atoms Ultracold trapped ions • Macroscopic quantum system • Single particle detection and at nano Kelvin temperature manipulation • Collective quantum states of 106 particles • Pristine source for quantum information • Very long coherence times processing & precision spectroscopy + Interactions Hybrid quantum system A new approach to • Ultracold collisions & quantum chemistry • Quantum information processing and decoherence • Quantum many-body physics with impurities • Metrology Review: C. Sias, M. Koehl, arXiv 1401.3188 Ion-neutral interactions An old problem in physics.. Ion-neutral collisions (1905) Ion-neutral interactions An old problem in physics.. Ion-neutral collisions (1905) Scattering from neutral- ion potential Ion-neutral interactions An old problem in physics.. Ion-neutral collisions (1905) Scattering from neutral- ion potential First atom-ion experiment (He+-Cs) Buffer gas sympathetic cooling First application: sympathetic cooling of charged particles Increase of confinment lifetime of Hg+ by buffer gas cooling (Ne) Buffer gas sympathetic cooling First application: sympathetic cooling of charged particles Increase of confinment lifetime of Hg+ by buffer gas cooling (Ne) Cooling of Ba+ by the presence of He buffer gas + theoretical analysis Ion-neutral quantum mixtures Can we exploit our knowledge in trapping and cooling particles to study collisions at lower temperature? Ion-neutral quantum mixtures Can we exploit our knowledge in trapping and cooling particles to study collisions at lower temperature? Yes! Ion-neutral quantum mixtures Can we exploit our knowledge in trapping and cooling particles to study collisions at lower temperature? Yes! A fast growing community + + + Yb-Yb Rb-Rb Rb-N2 Rb-Yb+ Rb-Ca+ Li-Ca+ Li-Yb+ Ca-Yb+ Ca-BaCl+ Rb-Ba+ Rb-Sr+ Rb-K+ Yb-Yb+ Na-Na+ .... Outline A brief intro of atom-ion collisions Hybrid atom-ion experiments – state-of-the-art Hybrid atom-ion experiments: perspectives Atom-ion systems for improving ion clocks Atom-ion interactions Charge-induced dipole interaction: R-4 scaling + - + Longer ranged than atom-atom interactions! R* ≳ 100nm For atom-atom interactions typically R*≈1nm Atom-ion interactions Charge-induced dipole interaction: R-4 scaling + - + Longer ranged than atom-atom interactions! R* ≳ 100nm For atom-atom interactions typically R*≈1nm Depends only from: - The ion’s charge Atom-ion interactions Charge-induced dipole interaction: R-4 scaling + - + Longer ranged than atom-atom interactions! R* ≳ 100nm For atom-atom interactions typically R*≈1nm Depends only from: - The ion’s charge - The DC polarizability of the neutral particle independent from the ion’s element! Atom-ion collisions First theory by Langevin (classical) 퐶 훼 푒2 4 퐶 = 푉 푟 = − 4 4 2 2 푟 4휋휀0 We can define a critical impact parameter 1/4 2 퐶4 푏푐 = 퐸푐 Large deflection 푏 < 푏푐 Small deflection 푏 > 푏푐 C. Zipkes, Ph.d. Thesis, University of Cambridge ..a bit of theory Colliding particles – Schroedinger eq. ℏ2 ℏ2푘2 − 훻2 + 푉 풓 Ψ 풓 = Ψ 풓 2휇 2휇 r Solution (at large r): In: plane wave Out: spherical wave 푒푖푘푟 Ψ 풓 ∼ 푒푖푘푧 + 푓(휃) 푟 ..a bit of theory Colliding particles – Schroedinger eq. ℏ2 ℏ2푘2 − 훻2 + 푉 풓 Ψ 풓 = Ψ 풓 z 2휇 2휇 Solution (at large r): In: plane wave Out: spherical wave 푒푖푘푟 Ψ 풓 ∼ 푒푖푘푧 + 푓(휃) 푟 Hypothesis: V(r) is central cylindrical simmetry Ok in atom-atom, atom-ion NOT in dipole-dipole! Noether theorem, a quantity is conserved: angular momentum ..a bit of theory Expansion in partial waves 푒푖푘푟 Ψ 풓 ∼ 푒푖푘푧 + 푓(휃) 푟 ..a bit of theory Expansion in partial waves 푒푖푘푟 Ψ 풓 ∼ 푒푖푘푧 + 푓(휃) 푟 (from expansion of spherical Bessel function) ∞ 1 푒푖푘푧 ∼ ෍ 2푙 + 1 푒푖푘푟 − −1 푙푒−푖푘푟 푃 cos 휃 2푖푘푟 푙 푙=0 ..a bit of theory Expansion in partial waves 푒푖푘푟 Ψ 풓 ∼ 푒푖푘푧 + 푓(휃) 푟 ∞ 푓 휃 = ෍ 2푙 + 1 푓푙푃푙 cos 휃 푙=0 ∞ 1 푒푖푘푧 ∼ ෍ 2푙 + 1 푒푖푘푟 − −1 푙푒−푖푘푟 푃 cos 휃 2푖푘푟 푙 푙=0 ..a bit of theory Expansion in partial waves 푒푖푘푟 Ψ 풓 ∼ 푒푖푘푧 + 푓(휃) Here is the physics 푟 ∞ 푓 휃 = ෍ 2푙 + 1 푓푙푃푙 cos 휃 푙=0 Legendre polynomials ∞ 1 푒푖푘푧 ∼ ෍ 2푙 + 1 푒푖푘푟 − −1 푙푒−푖푘푟 푃 cos 휃 2푖푘푟 푙 푙=0 1 Let’s re-write these terms 푓 = 푒푖훿푙 sin 훿 and solve the S.E. 푙 푘 푙 Incoming wave (crunch crunch..) Phase acquired in the collision 1 1 2푖훿푙 푖푘푟 푙 −푖푘푟 푅푙 푟 ∼ 푒 푒 − −1 푒 2푖푘푟 4휋 2푙 + 1 Scattered wave Radial part of Ψ 풓 ..a bit of theory 4휋 Cross section: 휎 = ෍ 2푙 + 1 sin 훿 2 푘2 푙 푙 ..a bit of theory 4휋 Cross section: 휎 = ෍ 2푙 + 1 sin 훿 2 푘2 푙 푙 Summarizing: a plane wave – written in terms of sum of spherical waves – is changed after the collision since each spherical wave of the expansion gets a different phase shift ..a bit of theory 4휋 Cross section: 휎 = ෍ 2푙 + 1 sin 훿 2 푘2 푙 푙 Summarizing: a plane wave – written in terms of sum of spherical waves – is changed after the collision since each spherical wave of the expansion gets a different phase shift Important: energy conservation! The only effect of collisions are phase shifts that modify the «envelope» of the wave but not its amplitude! ..a bit of theory How do we calculate the phase shifts? We solve the Schroedinger equation! (radial part) 1 푑2 푙 푙 + 1 2 휇 − 푟 + + 푉 푟 푅 푟 = 푘2푅 푟 푟 푑푟2 푟2 ℏ2 푙 푙 Inguscio, Fallani «Atomic Physics», Oxford University Press ..a bit of theory How do we calculate the phase shifts? We solve the Schroedinger equation! (radial part) 1 푑2 푙 푙 + 1 2 휇 − 푟 + + 푉 푟 푅 푟 = 푘2푅 푟 푟 푑푟2 푟2 ℏ2 푙 푙 Centrifugal barrier Inguscio, Fallani «Atomic Physics», Oxford University Press Atom-ion collisions Large deflection 푏 < 푏푐 Collisions from the hard wall Atom-ion collisions Large deflection Small deflection 푏 < 푏푐 푏 > 푏푐 Collisions from the Collisions from the hard wall centrifugal barrier Atom-ion collisions Large deflection Small deflection 푏 < 푏푐 푏 > 푏푐 Collisions from the Collisions from the hard wall centrifugal barrier 2 2퐶4 휎퐿 = 휋 푏푐 = 휋 퐸푐 (classical) Atom-ion collisions Large deflection Small deflection 푏 < 푏푐 푏 > 푏푐 Collisions from the Collisions from the hard wall centrifugal barrier 2 휋 휇퐶2 2 2퐶4 4 −1/3 휎퐿 = 휋 푏푐 = 휋 휎푡표푡 = 휋 1 + 2 퐸푐 퐸푐 16 ℏ (classical) (semiclassical) Atom-ion collisions Large deflection Small deflection 푏 < 푏푐 푏 > 푏푐 Collisions from the Collisions from the hard wall Random centrifugal barrier phase shift Integral of molecular potential 2 휋 휇퐶2 2 2퐶4 4 −1/3 휎퐿 = 휋 푏푐 = 휋 휎푡표푡 = 휋 1 + 2 퐸푐 퐸푐 16 ℏ (classical) (semiclassical) Atom-ion collisions Large deflection Small deflection 푏 < 푏푐 푏 > 푏푐 CollisionsLangevin from the Collisionssoft from the hardcollisions wall Random centrifugalcollisions barrier phase shift Integral of molecular potential 2 휋 휇퐶2 2 2퐶4 4 −1/3 휎퐿 = 휋 푏푐 = 휋 휎푡표푡 = 휋 1 + 2 퐸푐 퐸푐 16 ℏ (classical) (semiclassical) Atom-ion collisions 2 휋 휇퐶2 Cross section 휎 = 휋 1 + 4 퐸 −1/3 푡표푡 16 ℏ2 푐 Langevin cross 휎 = 휋 2퐶 퐸 −1/2 section 퐿 4 푐 R. Côté, A. Dalgarno, PRA 2000 Atom-ion collisions 2 휋 휇퐶2 Cross section 휎 = 휋 1 + 4 퐸 −1/3 푡표푡 16 ℏ2 푐 Langevin cross 휎 = 휋 2퐶 퐸 −1/2 section 퐿 4 푐 Scattering rate: 훾 = 푛 휎퐿푣 1/6 훾푡표푡 = 푛 휎푡표푡푣 ∝ 퐸푐 훾퐿 = 푛 휎퐿푣 = 푐표푠푡. R. Côté, A. Dalgarno, PRA 2000 Atom-ion collisions 2 휋 휇퐶2 Cross section 휎 = 휋 1 + 4 퐸 −1/3 푡표푡 16 ℏ2 푐 Langevin cross 휎 = 휋 2퐶 퐸 −1/2 section 퐿 4 푐 Scattering rate: 훾 = 푛 휎퐿푣 1/6 훾푡표푡 = 푛 휎푡표푡푣 ∝ 퐸푐 Independent from the 훾퐿 = 푛 휎퐿푣 = 푐표푠푡. collisional energy! R. Côté, A. Dalgarno, PRA 2000 Atom-ion collisions 2 휋 휇퐶2 Cross section 휎 = 휋 1 + 4 퐸 −1/3 푡표푡 16 ℏ2 푐 Langevin cross 휎 = 휋 2퐶 퐸 −1/2 section 퐿 4 푐 Scattering rate: 훾 = 푛 휎퐿푣 1/6 훾푡표푡 = 푛 휎푡표푡푣 ∝ 퐸푐 Independent from the 훾퐿 = 푛 휎퐿푣 = 푐표푠푡. collisional energy! At large collisional energies soft collisions are the most frequent R. Côté, A. Dalgarno, PRA 2000 Outline A brief intro of atom-ion collisions Hybrid atom-ion experiments – state-of-the-art Hybrid atom-ion experiments: perspectives Atom-ion systems for improving ion clocks The experiments Paul trap + Atom trap (Magneto-optical trap, magnetic trap, optical trap..) The experiments Paul trap + Atom trap (Magneto-optical trap, magnetic trap, optical trap..) Hudson group, UCLA The experiments Paul trap + Atom trap (Magneto-optical trap, magnetic trap, optical trap..) Hudson group, UCLA Ozeri group, Weizmann The experiments Paul trap + Atom trap (Magneto-optical trap, magnetic trap, optical trap..) Hudson group, UCLA Ozeri group,