Phases in addition to phase transitions of quantum materials

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Phases in addition to phase transitions of quantum materials

Miller, Paulette, News Director has reference to this Academic Journal, PHwiki organized this Journal Subir Sachdev Yale University Phases in addition to phase transitions of quantum materials Talk online: http://pantheon.yale.edu/~subir or Search as long as Sachdev on Phase changes in nature James Bay Winter Summer Ice Water At low temperatures, minimize energy At high temperatures, maximize entropy Classical physics: In equilibrium, at the absolute zero of temperature ( T = 0 ), all particles will reside at rest at positions which minimize their total interaction energy. This defines a (usually) unique phase of matter e.g. ice.

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Outline The quantum superposition principle – a qubit Interacting qubits in the laboratory – LiHoF4 Breaking up the Bose-Einstein condensate Bose-Einstein condensates in addition to superfluids The Mott insulator The cuprate superconductors Conclusions Varying “Planck’s constant” in the laboratory 1. The Quantum Superposition Principle The simplest quantum degree of freedom – a qubit Ho ions in a crystal of LiHoF4 These states represent e.g. the orientation of the electron spin on a Ho ion in LiHoF4 An electron with its “up-down” spin orientation uncertain has a definite “left-right” spin

2. Interacting qubits in the laboratory In its natural state, the potential energy of the qubits in LiHoF4 is minimized by or A Ferromagnet Enhance quantum effects by applying an external “transverse” magnetic field which prefers that each qubit point “right” For a large enough field, each qubit will be in the state Phase diagram g = strength of transverse magnetic field Absolute zero of temperature

Phase diagram g = strength of transverse magnetic field 3. Breaking up the Bose-Einstein condensate A. Einstein in addition to S.N. Bose (1925) Certain atoms, called bosons (each such atom has an even total number of electrons+protons+neutrons), condense at low temperatures into the same single atom state. This state of matter is a Bose-Einstein condensate. The Bose-Einstein condensate in a periodic potential “Eggs in an egg carton”

The Bose-Einstein condensate in a periodic potential “Eggs in an egg carton” The Bose-Einstein condensate in a periodic potential “Eggs in an egg carton” The Bose-Einstein condensate in a periodic potential “Eggs in an egg carton”

The Bose-Einstein condensate in a periodic potential “Eggs in an egg carton” Lowest energy state of a single particle minimizes kinetic energy by maximizing the position uncertainty of the particle The Bose-Einstein condensate in a periodic potential Lowest energy state as long as many atoms Large fluctuations in number of atoms in each potential well – superfluidity (atoms can “flow” without dissipation) The Bose-Einstein condensate in a periodic potential Lowest energy state as long as many atoms Large fluctuations in number of atoms in each potential well – superfluidity (atoms can “flow” without dissipation)

The Bose-Einstein condensate in a periodic potential Lowest energy state as long as many atoms Large fluctuations in number of atoms in each potential well – superfluidity (atoms can “flow” without dissipation) The Bose-Einstein condensate in a periodic potential Lowest energy state as long as many atoms Large fluctuations in number of atoms in each potential well – superfluidity (atoms can “flow” without dissipation) The Bose-Einstein condensate in a periodic potential Lowest energy state as long as many atoms Large fluctuations in number of atoms in each potential well – superfluidity (atoms can “flow” without dissipation)

The Bose-Einstein condensate in a periodic potential Lowest energy state as long as many atoms Large fluctuations in number of atoms in each potential well – superfluidity (atoms can “flow” without dissipation) The Bose-Einstein condensate in a periodic potential Lowest energy state as long as many atoms Large fluctuations in number of atoms in each potential well – superfluidity (atoms can “flow” without dissipation) 3. Breaking up the Bose-Einstein condensate By tuning repulsive interactions between the atoms, states with multiple atoms in a potential well can be suppressed. The lowest energy state is then a Mott insulator – it has negligible number fluctuations, in addition to atoms cannot “flow”

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3. Breaking up the Bose-Einstein condensate By tuning repulsive interactions between the atoms, states with multiple atoms in a potential well can be suppressed. The lowest energy state is then a Mott insulator – it has negligible number fluctuations, in addition to atoms cannot “flow” 3. Breaking up the Bose-Einstein condensate By tuning repulsive interactions between the atoms, states with multiple atoms in a potential well can be suppressed. The lowest energy state is then a Mott insulator – it has negligible number fluctuations, in addition to atoms cannot “flow” 3. Breaking up the Bose-Einstein condensate By tuning repulsive interactions between the atoms, states with multiple atoms in a potential well can be suppressed. The lowest energy state is then a Mott insulator – it has negligible number fluctuations, in addition to atoms cannot “flow”

Phase diagram Bose-Einstein Condensate 4. The cuprate superconductors A superconductor conducts electricity without resistance below a critical temperature Tc

Accessing quantum phases in addition to phase transitions by varying “Planck’s constant” in the laboratory Immanuel Bloch: Superfluid-to-insulator transition in trapped atomic gases Gabriel Aeppli: Seeing the spins (‘qubits’) in quantum materials by neutron scattering Aharon Kapitulnik: Superconductor in addition to insulators in artificially grown materials Matthew Fisher: Exotic phases of quantum matter

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