Abstract

Here, a dichotomy of particles and waves is employed in a quantum Monte Carlo calculation of interacting electrons. Through the creation and propagation of concurrent stochastic ensembles of walkers in physical space and in Hilbert space, one can correctly predict the ground state and the real-time evolution of a single electron interacting with a larger quantum system. It is shown that such walker ensembles can be constructed straightforwardly through a stochastic sampling (windowing) applied to the mean-field approximation. Our calculations reveal that the ground state and the real-time evolution of the probability distributions and the decoherence due to the Coulomb interaction in the presence of strong ultrashort laser pulses can be accounted for correctly by calculating the density matrix of the electron, without referencing the quantum many-body state of the whole system.

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References

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  1. T. Brabec, ed., Strong Field Laser Physics (Springer, 2008).
  2. M. Troyer and U. Wiese, “Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations,” Phys. Rev. Lett. 94, 170201 (2005).
    [Crossref]
  3. A. Montina, “Exponential complexity and ontological theories of quantum mechanics,” Phys. Rev. A 77, 022104 (2008).
    [Crossref]
  4. H. D. Meyer, U. Manthe, and L. S. Cederbaum, “The multi-configurational time-dependent Hartree approach,” Chem. Phys. Lett. 165, 73–78 (1990).
    [Crossref]
  5. B. Hammond, W. Lester, and P. Reynolds, Monte Carlo Methods in Ab Initio Quantum Chemistry (World Scientific, 1994).
  6. B. M. Austin, D. Y. Zubarev, and W. A. Lester, “Quantum Monte Carlo and related approaches,” Chem. Rev. 112, 263–288 (2012).
    [Crossref]
  7. G. Sugiyama and S. E. Koonin, “Auxiliary field Monte-Carlo for quantum many-body ground states,” Ann. Phys. 168, 1–26 (1986).
    [Crossref]
  8. I. P. Christov, “Correlated non-perturbative electron dynamics with quantum trajectories,” Opt. Express 14, 6906–6911 (2006).
    [Crossref]
  9. I. P. Christov, “Dynamic correlations with time-dependent quantum Monte Carlo,” J. Chem. Phys. 128, 244106 (2008).
    [Crossref]
  10. P. R. Holland, The Quantum Theory of Motion (Cambridge University, 1993).
  11. K. Molmer, Y. Castin, and J. Dalibard, “Monte Carlo wave-function method in quantum optics,” J. Opt. Soc. Am. 10, 524–538 (1993).
    [Crossref]
  12. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University, 2002).
  13. P. Deuar and P. Drummond, “First-principles quantum dynamics in interacting Bose gases: I. The positive P representation,” J. Phys. A 39, 1163–1168 (2006).
    [Crossref]
  14. I. P. Christov, “Double-slit interference with charged particles: density matrices and decoherence from time-dependent quantum Monte Carlo,” Phys. Scr. 91, 015402 (2015).
    [Crossref]
  15. R. P. Feynman, Statistical Mechanics (Benjamin, 1972).
  16. R. Grobe and J. H. Eberly, “Photoelectron spectra for two-electron system in a strong laser field,” Phys. Rev. Lett. 68, 2905–2908 (1992).
    [Crossref]
  17. I. P. Christov, “Molecular dynamics with time dependent quantum Monte Carlo,” J. Chem. Phys. 129, 214107 (2008).
    [Crossref]

2015 (1)

I. P. Christov, “Double-slit interference with charged particles: density matrices and decoherence from time-dependent quantum Monte Carlo,” Phys. Scr. 91, 015402 (2015).
[Crossref]

2012 (1)

B. M. Austin, D. Y. Zubarev, and W. A. Lester, “Quantum Monte Carlo and related approaches,” Chem. Rev. 112, 263–288 (2012).
[Crossref]

2008 (3)

A. Montina, “Exponential complexity and ontological theories of quantum mechanics,” Phys. Rev. A 77, 022104 (2008).
[Crossref]

I. P. Christov, “Dynamic correlations with time-dependent quantum Monte Carlo,” J. Chem. Phys. 128, 244106 (2008).
[Crossref]

I. P. Christov, “Molecular dynamics with time dependent quantum Monte Carlo,” J. Chem. Phys. 129, 214107 (2008).
[Crossref]

2006 (2)

P. Deuar and P. Drummond, “First-principles quantum dynamics in interacting Bose gases: I. The positive P representation,” J. Phys. A 39, 1163–1168 (2006).
[Crossref]

I. P. Christov, “Correlated non-perturbative electron dynamics with quantum trajectories,” Opt. Express 14, 6906–6911 (2006).
[Crossref]

2005 (1)

M. Troyer and U. Wiese, “Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations,” Phys. Rev. Lett. 94, 170201 (2005).
[Crossref]

1993 (1)

K. Molmer, Y. Castin, and J. Dalibard, “Monte Carlo wave-function method in quantum optics,” J. Opt. Soc. Am. 10, 524–538 (1993).
[Crossref]

1992 (1)

R. Grobe and J. H. Eberly, “Photoelectron spectra for two-electron system in a strong laser field,” Phys. Rev. Lett. 68, 2905–2908 (1992).
[Crossref]

1990 (1)

H. D. Meyer, U. Manthe, and L. S. Cederbaum, “The multi-configurational time-dependent Hartree approach,” Chem. Phys. Lett. 165, 73–78 (1990).
[Crossref]

1986 (1)

G. Sugiyama and S. E. Koonin, “Auxiliary field Monte-Carlo for quantum many-body ground states,” Ann. Phys. 168, 1–26 (1986).
[Crossref]

Austin, B. M.

B. M. Austin, D. Y. Zubarev, and W. A. Lester, “Quantum Monte Carlo and related approaches,” Chem. Rev. 112, 263–288 (2012).
[Crossref]

Breuer, H.-P.

H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University, 2002).

Castin, Y.

K. Molmer, Y. Castin, and J. Dalibard, “Monte Carlo wave-function method in quantum optics,” J. Opt. Soc. Am. 10, 524–538 (1993).
[Crossref]

Cederbaum, L. S.

H. D. Meyer, U. Manthe, and L. S. Cederbaum, “The multi-configurational time-dependent Hartree approach,” Chem. Phys. Lett. 165, 73–78 (1990).
[Crossref]

Christov, I. P.

I. P. Christov, “Double-slit interference with charged particles: density matrices and decoherence from time-dependent quantum Monte Carlo,” Phys. Scr. 91, 015402 (2015).
[Crossref]

I. P. Christov, “Molecular dynamics with time dependent quantum Monte Carlo,” J. Chem. Phys. 129, 214107 (2008).
[Crossref]

I. P. Christov, “Dynamic correlations with time-dependent quantum Monte Carlo,” J. Chem. Phys. 128, 244106 (2008).
[Crossref]

I. P. Christov, “Correlated non-perturbative electron dynamics with quantum trajectories,” Opt. Express 14, 6906–6911 (2006).
[Crossref]

Dalibard, J.

K. Molmer, Y. Castin, and J. Dalibard, “Monte Carlo wave-function method in quantum optics,” J. Opt. Soc. Am. 10, 524–538 (1993).
[Crossref]

Deuar, P.

P. Deuar and P. Drummond, “First-principles quantum dynamics in interacting Bose gases: I. The positive P representation,” J. Phys. A 39, 1163–1168 (2006).
[Crossref]

Drummond, P.

P. Deuar and P. Drummond, “First-principles quantum dynamics in interacting Bose gases: I. The positive P representation,” J. Phys. A 39, 1163–1168 (2006).
[Crossref]

Eberly, J. H.

R. Grobe and J. H. Eberly, “Photoelectron spectra for two-electron system in a strong laser field,” Phys. Rev. Lett. 68, 2905–2908 (1992).
[Crossref]

Feynman, R. P.

R. P. Feynman, Statistical Mechanics (Benjamin, 1972).

Grobe, R.

R. Grobe and J. H. Eberly, “Photoelectron spectra for two-electron system in a strong laser field,” Phys. Rev. Lett. 68, 2905–2908 (1992).
[Crossref]

Hammond, B.

B. Hammond, W. Lester, and P. Reynolds, Monte Carlo Methods in Ab Initio Quantum Chemistry (World Scientific, 1994).

Holland, P. R.

P. R. Holland, The Quantum Theory of Motion (Cambridge University, 1993).

Koonin, S. E.

G. Sugiyama and S. E. Koonin, “Auxiliary field Monte-Carlo for quantum many-body ground states,” Ann. Phys. 168, 1–26 (1986).
[Crossref]

Lester, W.

B. Hammond, W. Lester, and P. Reynolds, Monte Carlo Methods in Ab Initio Quantum Chemistry (World Scientific, 1994).

Lester, W. A.

B. M. Austin, D. Y. Zubarev, and W. A. Lester, “Quantum Monte Carlo and related approaches,” Chem. Rev. 112, 263–288 (2012).
[Crossref]

Manthe, U.

H. D. Meyer, U. Manthe, and L. S. Cederbaum, “The multi-configurational time-dependent Hartree approach,” Chem. Phys. Lett. 165, 73–78 (1990).
[Crossref]

Meyer, H. D.

H. D. Meyer, U. Manthe, and L. S. Cederbaum, “The multi-configurational time-dependent Hartree approach,” Chem. Phys. Lett. 165, 73–78 (1990).
[Crossref]

Molmer, K.

K. Molmer, Y. Castin, and J. Dalibard, “Monte Carlo wave-function method in quantum optics,” J. Opt. Soc. Am. 10, 524–538 (1993).
[Crossref]

Montina, A.

A. Montina, “Exponential complexity and ontological theories of quantum mechanics,” Phys. Rev. A 77, 022104 (2008).
[Crossref]

Petruccione, F.

H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University, 2002).

Reynolds, P.

B. Hammond, W. Lester, and P. Reynolds, Monte Carlo Methods in Ab Initio Quantum Chemistry (World Scientific, 1994).

Sugiyama, G.

G. Sugiyama and S. E. Koonin, “Auxiliary field Monte-Carlo for quantum many-body ground states,” Ann. Phys. 168, 1–26 (1986).
[Crossref]

Troyer, M.

M. Troyer and U. Wiese, “Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations,” Phys. Rev. Lett. 94, 170201 (2005).
[Crossref]

Wiese, U.

M. Troyer and U. Wiese, “Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations,” Phys. Rev. Lett. 94, 170201 (2005).
[Crossref]

Zubarev, D. Y.

B. M. Austin, D. Y. Zubarev, and W. A. Lester, “Quantum Monte Carlo and related approaches,” Chem. Rev. 112, 263–288 (2012).
[Crossref]

Ann. Phys. (1)

G. Sugiyama and S. E. Koonin, “Auxiliary field Monte-Carlo for quantum many-body ground states,” Ann. Phys. 168, 1–26 (1986).
[Crossref]

Chem. Phys. Lett. (1)

H. D. Meyer, U. Manthe, and L. S. Cederbaum, “The multi-configurational time-dependent Hartree approach,” Chem. Phys. Lett. 165, 73–78 (1990).
[Crossref]

Chem. Rev. (1)

B. M. Austin, D. Y. Zubarev, and W. A. Lester, “Quantum Monte Carlo and related approaches,” Chem. Rev. 112, 263–288 (2012).
[Crossref]

J. Chem. Phys. (2)

I. P. Christov, “Dynamic correlations with time-dependent quantum Monte Carlo,” J. Chem. Phys. 128, 244106 (2008).
[Crossref]

I. P. Christov, “Molecular dynamics with time dependent quantum Monte Carlo,” J. Chem. Phys. 129, 214107 (2008).
[Crossref]

J. Opt. Soc. Am. (1)

K. Molmer, Y. Castin, and J. Dalibard, “Monte Carlo wave-function method in quantum optics,” J. Opt. Soc. Am. 10, 524–538 (1993).
[Crossref]

J. Phys. A (1)

P. Deuar and P. Drummond, “First-principles quantum dynamics in interacting Bose gases: I. The positive P representation,” J. Phys. A 39, 1163–1168 (2006).
[Crossref]

Opt. Express (1)

Phys. Rev. A (1)

A. Montina, “Exponential complexity and ontological theories of quantum mechanics,” Phys. Rev. A 77, 022104 (2008).
[Crossref]

Phys. Rev. Lett. (2)

M. Troyer and U. Wiese, “Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations,” Phys. Rev. Lett. 94, 170201 (2005).
[Crossref]

R. Grobe and J. H. Eberly, “Photoelectron spectra for two-electron system in a strong laser field,” Phys. Rev. Lett. 68, 2905–2908 (1992).
[Crossref]

Phys. Scr. (1)

I. P. Christov, “Double-slit interference with charged particles: density matrices and decoherence from time-dependent quantum Monte Carlo,” Phys. Scr. 91, 015402 (2015).
[Crossref]

Other (5)

R. P. Feynman, Statistical Mechanics (Benjamin, 1972).

H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University, 2002).

P. R. Holland, The Quantum Theory of Motion (Cambridge University, 1993).

T. Brabec, ed., Strong Field Laser Physics (Springer, 2008).

B. Hammond, W. Lester, and P. Reynolds, Monte Carlo Methods in Ab Initio Quantum Chemistry (World Scientific, 1994).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the transition from the mean-field approximation where all Monte Carlo walkers are guided by the same wave function to the TDQMC representation where each walker is guided by its own guide wave.

Fig. 2.
Fig. 2.

Energy of the ground state of a 1D helium atom as function of the parameter α of Eq. (13), with corresponding error bars (for 20 consecutive runs). The rightmost point shows the transition to the mean-field ground state energy.

Fig. 3.
Fig. 3.

Snapshot of the walker distribution for (a) the ground state and (b) the corresponding smoothed distribution (red line). The blue line in (b) depicts the exact ground state.

Fig. 4.
Fig. 4.

Contour maps of (a) the moduli of the density matrices for the ground state and (b) after free diffraction of the interacting electron waves. Exact result—blue contours; TDQMC result—red contours.

Fig. 5.
Fig. 5.

(a) Survival probability for a single electron in a one-dimensional helium atom exposed to a powerful ultrashort laser pulse, and (b) the quantum coherence calculated as sum of the antidiagonal elements of the density matrix in coordinate representation. Red lines—from TDQMC; blue lines—exact result.

Equations (27)

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i t Ψ ( R , t ) = 2 2 m 2 Ψ ( R , t ) + V ( R , t ) Ψ ( R , t ) ,
V ( r 1 , , r N , t ) = V e n ( r 1 , , r N ) + V e e ( r 1 , , r N ) + V ext ( r 1 , , r N , t ) = k = 1 N V e n ( r k ) + k > l N V e e ( r k r l ) + V ext ( r 1 , , r N , t ) .
Ψ ( r 1 , r 2 , , r N , t ) = i = 1 N ϕ i ( r i , t )
i t ϕ i ( r i , t ) = [ 2 2 m i 2 + V e n ( r i ) + V ext ( r i , t ) + V e e Hartree ( r i , t ) ] ϕ i ( r i , t ) ,
V e e Hartree ( r i , t ) = j i N 1 d r j | ϕ j ( r j , t ) | 2 × d r j | ϕ j ( r j , t ) | 2 V e e ( r i r j )
K [ r j , r j k ( t ) , σ j k ] = exp ( | r j r j k ( t ) | 2 2 σ j k ( r j k , t ) 2 ) .
| ϕ j ( r j , t ) | 2 | ϕ j k ( r j , t ) | 2 | ϕ j k ( r j , t ) | 2 K [ r j , r j k ( t ) , σ j k ] ,
V e e eff ( r i , t ) = j i N 1 d r j | ϕ j k ( r j , t ) | 2 K [ r j , r j k ( t ) , σ j k ] × d r j | ϕ j k ( r j , t ) | 2 K [ r j , r j k ( t ) , σ j k ] V e e ( r i r j ) ,
i t ϕ i k ( r i , t ) = [ 2 2 m i 2 + V e n ( r i ) + V ext ( r i , t ) + V e e eff ( r i , t ) ] ϕ i k ( r i , t ) .
V e e eff ( r i , t ) = j i N 1 Z j k l M V e e [ r i r j l ( t ) ] K [ r j l ( t ) , r j k ( t ) , σ j k ] ,
Z j k = l M K [ r j l ( t ) , r j k ( t ) , σ j k ] .
v i k ( t ) = d r i k ( t ) d t = m Im [ 1 ϕ i k ( r i , t ) i ϕ i k ( r i , t ) ] r i = r i k ( t ) ,
σ j k ( r j k , t ) = α j . σ j ( t ) ,
d r i k ( t ) = v i k ( t ) d t + η ( t ) m d t ,
ρ i ( r i , r i , t ) = 1 M k = 1 M ϕ i k * ( r i , t ) ϕ i k ( r i , t ) ,
ρ 2 ( r 1 , r 2 , t ) = | Ψ ( R , t ) | 2 d r 3 d r N ,
P ( u , t ) = ρ 2 ( r 1 , r 2 , t ) δ [ ( r 1 r 2 ) u ] d r 1 d r 2 ,
P ( u , t ) k = 1 M K k [ | r 12 k ( t ) u | σ 12 ] ,
E loc k = i = 1 N [ 2 2 m i 2 ϕ i k ( r i k ) ϕ i k ( r i k ) + V e n ( r i k ) ] + i > j N V e e ( r i k r j k ) | r i k = r i k ( t ) r j k = r j k ( t ) .
i t Ψ ( x 1 , x 2 , t ) = [ H 0 + V e e ( x 1 x 2 ) + V ext ( x 1 , x 2 , t ) ] Ψ ( x 1 , x 2 , t ) ,
H 0 = 1 2 2 x 1 2 1 2 2 x 2 2 a 1 + x 1 2 a 1 + x 2 2 ,
V e e ( x 1 x 2 ) = b 1 + ( x 1 x 2 ) 2 .
i t ϕ i k ( x i , t ) = [ 1 2 i 2 a 1 + x i 2 + V e e eff ( x i , t ) + V ext ( x i , t ) ] ϕ i k ( x i , t ) ,
V e e eff ( x i , t ) = j i 2 1 Z j k l = 1 M b 1 + [ x i x j l ( t ) ] 2 × exp ( | x j l ( t ) x j k ( t ) | 2 2 σ j k ( x j k , t ) 2 ) ,
Z j k = l = 1 M exp ( | x j l ( t ) x j k ( t ) | 2 2 σ j k ( x j k , t ) 2 ) .
ρ 1 ( x 1 , x 1 , t ) = 1 M k = 1 M ϕ 1 k * ( x 1 , t ) ϕ 1 k ( x 1 , t ) ,
ρ ( x , x , t ) = Ψ ( x , x 1 , t ) Ψ * ( x , x 1 , t ) d x 1 Ψ ( x , x 1 , t ) Ψ * ( x , x 1 , t ) d x 1 d x .

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