Fast adiabatic cooling procedures have important implications for the attainability of absolute zero. While traditionally adiabatically cooling a system is associated with slow thermal processes, for the parametric quantum harmonic oscillator fast frictionless processes are known, which transfer a system from an initial thermal equilibrium at one temperature into thermal equilibrium at another temperature. This makes such systems special tools in analyzing the bounds on fast cooling procedures. Previous discussions of those systems used frictionless cooling assuming real frequencies of the oscillator. Using a control with imaginary frequencies (repulsive potential) revises previous implications for the possible operation of a quantum refrigerator. Here we discuss these requisite revisions in the context of the third law of thermodynamics. In addition to minimum time controls, which are always of the bang-bang form, fast frictionless processes with a continuous variation of the frequency have been presented previously in the literature. Such continuous variation controls have been experimentally verified by cooling a Bose-Einstein condensate, while minimum time controls still await verification. As some implementations may indeed not be able to implement the instantaneous jumps in frequency required by bang-bang controls, constraining the rate of change in the frequency calls for ramped bang-bang solutions. We present such solutions and compare their performance to the continuous controls used in the experiment.Fast adiabatic cooling procedures have important implications for the attainability of absolute zero. While traditionally adiabatically cooling a system is associated with slow thermal processes, for the parametric quantum harmonic oscillator fast frictionless processes are known, which transfer a system from an initial thermal equilibrium at one temperature into thermal equilibrium at another temperature. This makes such systems special tools in analyzing the bounds on fast cooling procedures. Previous discussions of those systems used frictionless cooling assuming real frequencies of the oscillator. Using a control with imaginary frequencies (repulsive potential) revises previous implications for the possible operation of a quantum refrigerator. Here we discuss these requisite revisions in the context of the third law of thermodynamics. In addition to minimum time controls, which are always of the bang-bang form, fast frictionless processes with a continuous variation of the frequency have been presented previously in the literature. Such continuous variation controls have been experimentally verified by cooling a Bose-Einstein condensate, while minimum time controls still await verification. As some implementations may indeed not be able to implement the instantaneous jumps in frequency required by bang-bang controls, constraining the rate of change in the frequency calls for ramped bang-bang solutions. We present such solutions and compare their performance to the continuous controls used in the experiment.

Europhysics Letters (EPL)Dec 1, 201173 citations

Towards thermalization

Yun Li

Nature PhysicsApr 24, 20180 citations

Thermalization of fast cesium 5D3∕2 atoms in collisions with ground-state cesium atoms

Aaron Marks, A. P. Hickman, Alan D. Streater +1 more

We have investigated collisions involving fast, excited Cs atoms produced by photodissociating ${\mathrm{Cs}}_{2}$ molecules with a pulsed dye laser. The velocities of the atoms in the $5D$ state formed by the process ${\mathrm{Cs}}_{2}(X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+})+\ensuremath{\hbar}{\ensuremath{\omega}}_{\text{pump}}\ensuremath{\rightarrow}{\mathrm{Cs}}_{2}^{*}\ensuremath{\rightarrow}\mathrm{Cs}(5D)+\mathrm{Cs}(6S)$ are much greater than typical thermal velocities associated with the cell temperature. Using a narrow-band cw probe laser to observe the increased Doppler broadening of the $5{D}_{3∕2}\ensuremath{\rightarrow}5{F}_{5∕2}$ excitation line shape, we are able to monitor the time evolution of the velocity distribution of these $5D$ atoms. We analyze the data using a model that predicts the time-dependent excitation line shape of the fast atoms. Because the photons used to dissociate the molecules have a well-defined energy, the velocity distribution of the excited atoms in the early time after they are produced can be fairly well determined. Over time, velocity-changing collisions with ground-state Cs atoms cause the velocity distribution of excited atoms to approach the thermal limit. An analysis based on the strong-collision model leads to a prediction that the observed line shape at intermediate times will be a linear combination of contributions from distinct ``fast'' and ``thermalized'' atomic populations. By fitting our data to this model, a rate coefficient for velocity-changing collisions of fast $\mathrm{Cs}(5{D}_{3∕2})$ atoms with ground-state Cs atoms has been determined. The result ${k}_{\mathrm{VCC}}=(6.1\ifmmode\pm\else\textpm\fi{}1.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}\phantom{\rule{0.2em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ corresponds to an effective velocity-changing collision cross section of ${\ensuremath{\sigma}}_{\mathrm{VCC}}^{\mathrm{Cs},\mathrm{eff}}=(1.2\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{2}$.We have investigated collisions involving fast, excited Cs atoms produced by photodissociating ${\mathrm{Cs}}_{2}$ molecules with a pulsed dye laser. The velocities of the atoms in the $5D$ state formed by the process ${\mathrm{Cs}}_{2}(X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+})+\ensuremath{\hbar}{\ensuremath{\omega}}_{\text{pump}}\ensuremath{\rightarrow}{\mathrm{Cs}}_{2}^{*}\ensuremath{\rightarrow}\mathrm{Cs}(5D)+\mathrm{Cs}(6S)$ are much greater than typical thermal velocities associated with the cell temperature. Using a narrow-band cw probe laser to observe the increased Doppler broadening of the $5{D}_{3∕2}\ensuremath{\rightarrow}5{F}_{5∕2}$ excitation line shape, we are able to monitor the time evolution of the velocity distribution of these $5D$ atoms. We analyze the data using a model that predicts the time-dependent excitation line shape of the fast atoms. Because the photons used to dissociate the molecules have a well-defined energy, the velocity distribution of the excited atoms in the early time after they are produced can be fairly well determined. Over time, velocity-changing collisions with ground-state Cs atoms cause the velocity distribution of excited atoms to approach the thermal limit. An analysis based on the strong-collision model leads to a prediction that the observed line shape at intermediate times will be a linear combination of contributions from distinct ``fast'' and ``thermalized'' atomic populations. By fitting our data to this model, a rate coefficient for velocity-changing collisions of fast $\mathrm{Cs}(5{D}_{3∕2})$ atoms with ground-state Cs atoms has been determined. The result ${k}_{\mathrm{VCC}}=(6.1\ifmmode\pm\else\textpm\fi{}1.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}\phantom{\rule{0.2em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ corresponds to an effective velocity-changing collision cross section of ${\ensuremath{\sigma}}_{\mathrm{VCC}}^{\mathrm{Cs},\mathrm{eff}}=(1.2\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{2}$.

Physical Review AJan 19, 20051 citation

New horizons towards thermalization

Nature PhysicsSep 25, 20181 citation

Thermal Noise on Adiabatic Quantum Computation

Man‐Hong Yung

The success of adiabatic quantum computation (AQC) depends crucially on the ability to maintain the quantum computer in the ground state of the evolution Hamiltonian. The computation process has to be sufficiently slow as restricted by the minimal energy gap. However, at finite temperatures, it might need to be fast enough to avoid thermal excitations. The question is, how fast does it need to be? The structure of evolution Hamiltonians for AQC is generally too complicated for answering this question. Here we model an adiabatic quantum computer as a (parametrically driven) harmonic oscillator. The advantages of this model are (1) it offers high flexibility for quantitative analysis on the thermal effect, (2) the results qualitatively agree with previous numerical calculation, and (3) it could be experimentally verified with quantum electronic circuits.The success of adiabatic quantum computation (AQC) depends crucially on the ability to maintain the quantum computer in the ground state of the evolution Hamiltonian. The computation process has to be sufficiently slow as restricted by the minimal energy gap. However, at finite temperatures, it might need to be fast enough to avoid thermal excitations. The question is, how fast does it need to be? The structure of evolution Hamiltonians for AQC is generally too complicated for answering this question. Here we model an adiabatic quantum computer as a (parametrically driven) harmonic oscillator. The advantages of this model are (1) it offers high flexibility for quantitative analysis on the thermal effect, (2) the results qualitatively agree with previous numerical calculation, and (3) it could be experimentally verified with quantum electronic circuits.

arXiv:0807.4819Jul 30, 20084 citations

We have investigated collisions involving fast, excited Cs atoms produced by photodissociating

{\mathrm{Cs}}_{2}

molecules with a pulsed dye laser. The velocities of the atoms in the

5D

state formed by the process ${\mathrm{Cs}}_{2}(X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+})+\ensuremath{\hbar}{\ensuremath{\omega}}_{\text{pump}}\ensuremath{\rightarrow}{\mathrm{Cs}}_{2}^{*}\ensuremath{\rightarrow}\mathrm{Cs}(5D)+\mathrm{Cs}(6S)$ are much greater than typical thermal velocities associated with the cell temperature. Using a narrow-band cw probe laser to observe the increased Doppler broadening of the $5{D}_{3∕2}\ensuremath{\rightarrow}5{F}_{5∕2}$ excitation line shape, we are able to monitor the time evolution of the velocity distribution of these

5D

atoms. We analyze the data using a model that predicts the time-dependent excitation line shape of the fast atoms. Because the photons used to dissociate the molecules have a well-defined energy, the velocity distribution of the excited atoms in the early time after they are produced can be fairly well determined. Over time, velocity-changing collisions with ground-state Cs atoms cause the velocity distribution of excited atoms to approach the thermal limit. An analysis based on the strong-collision model leads to a prediction that the observed line shape at intermediate times will be a linear combination of contributions from distinct ``fast'' and ``thermalized'' atomic populations. By fitting our data to this model, a rate coefficient for velocity-changing collisions of fast

\mathrm{Cs}(5{D}_{3∕2})

atoms with ground-state Cs atoms has been determined. The result ${k}_{\mathrm{VCC}}=(6.1\ifmmode\pm\else\textpm\fi{}1.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}\phantom{\rule{0.2em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ corresponds to an effective velocity-changing collision cross section of ${\ensuremath{\sigma}}_{\mathrm{VCC}}^{\mathrm{Cs},\mathrm{eff}}=(1.2\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{2}$.