Quantum critical behavior influenced by measurement backaction in ultracold gases

Abstract

Recent realizations of quantum gas microscope offer the possibility of continuous monitoring of the dynamics of a quantum many-body system at the single-particle level. By analyzing effective non-Hermitian Hamiltonians of interacting bosons in an optical lattice and continuum, we demonstrate that the backaction of quantum measurement shifts the quantum critical point and gives rise to a unique critical phase beyond the terrain of the standard universality class. We perform meanfield and strong-coupling-expansion analyses and show that non-Hermitian contributions shift the superfluid-to-Mott-insulator transition point. Using a low-energy effective field theory, we discuss critical behavior of the one-dimensional interacting Bose gas subject to the measurement backaction. We derive an exact ground state of the effective non-Hermitian Hamiltonian and find a unique critical behavior beyond the Tomonaga-Luttinger liquid universality class. We propose experimental implementations of post-selections using quantum gas microscopes to simulate the non-Hermitian dynamics and argue that our results can be investigated with current experimental techniques in ultracold atoms.

Theory of Non-Hermitian Fermionic Superfluidity with a Complex-Valued Interaction

“…Finally, we note that the NH dynamics is faithfully realized when we perform a quantum-gas-microscopy measurement of an atom number and then postselect the measurement outcome which does not contain any atom loss [5,6]. Since the quantum-gas microscopy for the attractive Hubbard model was already realized [57], this method can also be used for an unambiguous observation of NH superfluidity.…”

“…Such theoretical predictions have been confirmed experimentally by using optical systems and ultracold atoms [22][23][24][25][26][27][28][29][30]. However, since most of the previous studies dealt with single-particle physics, exploration of many-body physics in NH systems is still in its infancy [3][4][5][6][31][32][33][34].…”

“…NH quantum systems arise when the system undergoes dissipation to an environment [37,38]. It has been revealed that non-Hermiticity drastically alters the properties of a number of quantum phenomena that have been established in the Hermitian physics, such as quantum phase transitions [1][2][3][4], quantum critical behavior [5][6][7], topological phases [8][9][10][11][12][13][14][15][16][17], and magnetism [18]. Such theoretical predictions have been confirmed experimentally by using optical systems and ultracold atoms [22][23][24][25][26][27][28][29][30].…”

Non-Hermitian fractional quantum Hall states

“…Here e x(y) denotes the unit vector for each direction, and the lattice constant is set to unity. When we focus on the short-time evolution, the last term describing the quantum-jump is negligible [61][62][63][64]. In this case, we can see that the timeevolution is described by…”

“…Let us start with the definitions of the ground states and the energy gap because the energy spectrum of the non-Hermitian Hamiltonian becomes complex. We define the ground states with the minimum value of the real-part [61]. For our system, these states also have the longest lifetime τ (∼ −1/ImE with ImE < 0).…”