S. Kallush - Academia.edu (original) (raw)

Papers by S. Kallush

Springer Series in Chemical Physics, 2009

Physical Review A, 2012

We describe quantum dynamical calculations of ultracold 85 Rb trap-loss collisions induced by pul... more We describe quantum dynamical calculations of ultracold 85 Rb trap-loss collisions induced by pulses of light whose frequency is chirped on the nanosecond time scale. The chirped light excites the ground-state collisional wave function to the long-range attractive potential and escape from the trap is modeled by an absorbing boundary at short range. Both positive and negative chirps are considered and various chirp shapes and detunings are examined. For positive chirps, the loss rates are rather independent of the chirp shape. Negative chirps, on the other hand, show a dependence on chirp shape for detunings where collisional flux can be coherently returned to the ground state. These trends are consistent with the results of a recent experiment.

Physical Review A, 2011

We present results on coherent control of ultracold trap-loss collisions using 40 ns pulses of no... more We present results on coherent control of ultracold trap-loss collisions using 40 ns pulses of nonlinearly frequency-chirped light. The chirps, either positive or negative, sweep ∼ 1 GHz in 100 ns and are centered at various detunings below the D2 line of 85 Rb. At each center detuning, we compare the collisional rate constant β for chirps that are linear in time, concave-down and concave-up. For positive chirps, we find that β generally depends very little on the shape of the chirp. For negative chirps, however, we find that β can be enhanced by up to 50(20)% for the case of the concave-down shape. This occurs at detunings where the evolution of the wavepacket is expected to be coherent. An enhancement at these detunings is also seen in quantum mechanical simulations of the collisional process.

A description of photoassociation by CW laser is formulated in the framework of grid methods. The... more A description of photoassociation by CW laser is formulated in the framework of grid methods. The Hamiltonian describing one or several bound states coupled to a multiple of continuum manifolds via a radiative field is written in the energy representation and diagonalized. The generality of the treatment allows to compute accurately and efficiently physical properties such as non-linear high-intensity energy shifts, line shapes, and photoassociation rates both for isolated and non-isolated resonances. Application is given to sodium photoassociation in the experimental conditions of Mc Kenzie et al [Phys. Rev. Lett. 88, 090403 (2002)]. Inverted region for the dependency of the rate vs. the intensity and non-symmetric lineshapes were predicted to occur above the saturation limit. Comparison with the model of Bohn and Julienne [Phys. Rev. A 60, 414 (1999)] is discussed. PACS numbers:

ABSTRACT We report on the results of quantum calculations of ^87Rb2 formation from ultracold atom... more ABSTRACT We report on the results of quantum calculations of ^87Rb2 formation from ultracold atoms by pulses of frequency-chirped light on the nanosecond timescale. This time-dependent photoassociation is modeled by following the dynamics of the collisional wave functions on both ground-state and excited-state potentials in the presence of the chirped light. Because of the relatively long time scales involved, spontaneous emission from the excited state must be accounted for. Results of the calculations are compared to recent measurements made with 40 ns FWHM Gaussian pulses and chirps that sweep 1 GHz in 100 ns. Dependencies on pulse intensity and chirp direction will be presented. This work is supported by DOE.

Physical Review A, 2007

We demonstrate the ability to coherently control ultracold atomic Rb collisions using frequency-c... more We demonstrate the ability to coherently control ultracold atomic Rb collisions using frequency-chirped light on the nanosecond time scale. For certain center frequencies of the chirp, the rate of inelastic trap-loss collisions induced by negatively chirped light is dramatically suppressed compared to the case of a positive chirp. We attribute this to a fundamental asymmetry in the system: an excited wave packet moves inward on the attractive molecular potential. For a positive chirp, the resonance condition moves outward in time, while for a negative chirp, it moves inward, in the same direction as the excited wave packet; this allows multiple interactions between the wave packet and the light, enabling the wave packet to be returned coherently to the ground state. Classical and quantum calculations support this interpretation.

Physical Review A, 2011

The major task in quantum control theory is to find an external field that transforms the system ... more The major task in quantum control theory is to find an external field that transforms the system from one state to another or executes a predetermined unitary transformation. We investigate the difficulty of computing the control field as the size of the Hilbert space is increased. In the models studied the controls form a small closed subalgebra of operators. Complete controllability is obtained by the commutators of the controls with the stationary Hamiltonian. We investigate the scaling of the computation effort required to converge a solution for the quantum control task with respect to the size of the Hilbert space. The models studied include the double-well Bose Hubbard model with the SU(2) control subalgebra and the Morse oscillator with the Heisenberg-Weil algebra. We find that for initial and target states that are classified as generalized coherent states (GCSs) of the control subalgebra the control field is easily found independent of the size of the Hilbert space. For such problems, a control field generated for a small system can serve as a pilot for finding the field for larger systems. Attempting to employ pilot fields that generate superpositions of GCSs or cat states failed. No relation was found between control solutions of different Hilbert space sizes. In addition the task of finding such a field scales unfavorably with Hilbert space sizes. We demonstrate the use of symmetry to obtain quantum transitions between states without phase information. Implications to quantum computing are discussed. 10 J = 5 J = 10 J = 20 J = 40 J = 80 J = 160 J = 320

Chemical Physics Letters, 2006

The origin of an artifact known as the appearance of ghost states in mapped Fourier grid methods ... more The origin of an artifact known as the appearance of ghost states in mapped Fourier grid methods is investigated. It was found that the ghost states can be attributed to under sampling of the high momentum components which are folded from the inner to the outer region of the potential to create the ghosts. The effect was corrected by addition of a complex potential at the outer region. The exterior complex potential was shown to shift the ghost states to the continuum part of the spectrum in a controllable way. The various methods to improve the mapped grid method are discussed in this context, and the use of zero boundary conditions is shown to be not essential.

Physical Review A - Atomic, Molecular, and Optical Physics, 2008

Bound-state molecules can be photoassociated directly from ultracold free-atom pairs by excitatio... more Bound-state molecules can be photoassociated directly from ultracold free-atom pairs by excitation to a purely repulsive electronic state. The process is explained on the basis of quantum unitarity: the initially free-scattering state is transformed by an impulsive light pulse to a deformed superposition which contains bound-state components. For pulse durations which are short compared to the ultracold dynamics, the maximal rate of photoassociation was found to be determined by the initial stationary distribution of scattering states of the atom pairs. The process was simulated for an ultracold gas of Rb with a temperature of T=44 K and a density of 10¹¹ cm³. Transform-limited pulses maximize the photoassociation, yielding 1 bound molecule per pulse. Coherent control calculated by a local control scheme can increase the photoassociation yield by two orders of magnitude.

Physical Review A, 2013

We use frequency-chirped light on the nanosecond time scale to produce ultracold 87 Rb2 molecules... more We use frequency-chirped light on the nanosecond time scale to produce ultracold 87 Rb2 molecules in the lowest triplet state via the process of photoassociation. Comparing to quantum simulations of the molecular formation, we conclude that coherent stimulated emission plays an important role and is primarily responsible for the significant difference observed between positive and negative chirps.

Physical Review A, 2012

Quantum control tasks are classified either as classical-like or as quantum requiring interferenc... more Quantum control tasks are classified either as classical-like or as quantum requiring interference of pathways. We study the generation of interference pathways and relate them to the fidelity of the control target at a fixed time for various tasks. The model drift Hamiltonian studied is the two-dimensional Henon-Heiles (HH) potential. This system shows regular classical dynamics for low energies and chaotic dynamics for higher energies. A control operator supported by the whole momentum space and therefore connecting the entire Hilbert phase space is a random spiky potential. The other extreme is a smooth control potential. Intermediate cases are obtained by filtering the random spiky potential in momentum space. The fidelity of achieving a control task was related to the connectivity in phase space of the control operators. Typical quantum tasks such as generating a superposition of generalized coherent states rely on interfering pathways. For these cases the nonlinearity in the drift or control Hamiltonian is a necessary requirement for creating interferences. Control over rapidly diverging components of the wave function is achieved by the use of highly nonlocal control operators. Quantum control under chaotic drift was found to give a better yield than control under regular dynamics for such cases. For classical tasks we study the transformation of an initial generalized coherent state to another one. The best fidelity is obtained for regular or harmonic regions of the potential and smooth control operators. The approach to the classical limit is checked by decreasing the effective value ofh. Control under both quantum and classical tasks suffered from the decrease ofh and the approach to classical proximity. Classical control tasks which rely heavily on maintaining a generalized coherent state throughout the evolution were found to be dysfunctional and lead to a completely uncontrolled situation once the classical chaos starts to appear.

Physical Review A, 2006

The problem of automatically protecting a quantum system against noise in a closed circuit is ana... more The problem of automatically protecting a quantum system against noise in a closed circuit is analyzed. A general scheme is developed built from two steps. At first, a distillation step is induced in which undesired components are removed to another degree of freedom of the system. Later a recovering step is employed which the system gains back its initial density. An Optimal-Control method is used to generate the distilling operator. The scheme is demonstrated by a simulation of a two level byte influenced by white noise. Undesired deviations from the target were shown to be reduced by at least two orders of magnitude on average. The relations between the quantum version of the classical Watt's Governor and the field of quantum information are also discussed.

Physical Chemistry Chemical Physics, 2010

The well-documented propensity of negatively-chirped pulses to enhance resonant impulsive Raman s... more The well-documented propensity of negatively-chirped pulses to enhance resonant impulsive Raman scattering has been rationalized in terms of a one pulse pump-dump sequence which "follows" the evolution of the excited molecules and dumps them back at highly displaced configurations. The aim of this study was to extend the understanding of this effect to molecules with many displaced vibrational modes in the presence of condensed surroundings. In particular, to define an optimally chirped pulse, to investigate what exactly it "follows" and to discover how this depends on the molecule under study. To this end, linear chirp effects on vibrational coherences in poly-atomics are investigated experimentally and theoretically. Chirped pump-impulsive probe experiments are reported for Sulforhodamine-B ("Kiton Red"), Betaine-30 and Oxazine-1 in ethanol solutions with <10 fs resolution. Numerical simulations, including numerous displaced modes and electronic dephasing, are conducted to reproduce experimental results. Through semi-quantitative reproduction of experimental results in all three systems we show that the effect of group velocity dispersion (GVD) on the buildup of ground state wave-packets depends on the pulse spectrum, on the displacements of vibrational modes upon excitation, on the detuning of the excitation pulses from resonance, and on electronic dephasing rates. Akin to scenarios described for frequency-domain resonance Raman, within the small-displacement regime each mode responds to excitation chirp independently and the optimal GVD is mode-specific. Highly-displaced modes entangle the dynamics of excitation in different modes, requiring a multi-dimensional description of the response. Rapid photochemistry and ultrafast electronic dephasing narrow the window of opportunity for coherent manipulations, leading to a reduced and similar optimal chirp for different modes. Finally, non-intuitive coherent aspects of chirp "following" are predicted in the small-displacement and slow-dephasing regime, which remain to be observed in experiment.

Chemical Physics Letters, 2004

A fully-selective population transfer scheme for diatomic molecules using short-duration (<ns) la... more A fully-selective population transfer scheme for diatomic molecules using short-duration (<ns) laser pulses is developed via the concept of light-induced potentials. It explicitly takes rotational degrees of freedom into account. We apply it to a specific Na 2 transition from the lowest ro-vibrationic state to a single ro-vibrational state of a doubly excited electronic state via an intermediate electronic state. The process insures total selective population transfer with pulses short compared to the molecule rotation time. However, an estimate of the multiphoton ionization rate using time-dependent density functional theory suggests that ionization may significantly adversely affect the transfer.

Quantum control with noisy fields: computational complexity vs. sensitivity to noise Abstract. A ... more Quantum control with noisy fields: computational complexity vs. sensitivity to noise Abstract. A closed quantum system is defined as completely controllable if an arbitrary unitary transformation can be executed using the available controls. In practice, control fields are a source of unavoidable noise, which has to be suppressed to retain controllability. Can one design control fields such that the effect of noise is negligible on the time-scale of the transformation? This question is intimately related to the fundamental problem of a connection between the computational complexity of the control problem and the sensitivity of the controlled system to noise. The present study considers a paradigm of control, where the Lie-algebraic structure of the control Hamiltonian is fixed, while the size of the system increases with the dimension of the Hilbert space representation of the algebra. We find two types of control tasks, easy and hard. Easy tasks are characterized by a small variance of the evolving state with respect to the operators of the control operators. They are relatively immune to noise and the control field is easy to find. Hard tasks have a large variance, are sensitive to noise and the control field is hard to find. The influence of noise increases with the size of the system, which is measured by the scaling factor N of the largest weight of the representation. For fixed time and control field as O(N ) for easy tasks and as O(N 2 ) for hard tasks. As a consequence, even in the most favorable estimate, for large quantum systems, generic noise in the controls dominates for a typical class of target transformations, i.e., complete controllability is destroyed by noise.

Springer Series in Chemical Physics, 2009

Physical Review A, 2012

We describe quantum dynamical calculations of ultracold 85 Rb trap-loss collisions induced by pul... more We describe quantum dynamical calculations of ultracold 85 Rb trap-loss collisions induced by pulses of light whose frequency is chirped on the nanosecond time scale. The chirped light excites the ground-state collisional wave function to the long-range attractive potential and escape from the trap is modeled by an absorbing boundary at short range. Both positive and negative chirps are considered and various chirp shapes and detunings are examined. For positive chirps, the loss rates are rather independent of the chirp shape. Negative chirps, on the other hand, show a dependence on chirp shape for detunings where collisional flux can be coherently returned to the ground state. These trends are consistent with the results of a recent experiment.

Physical Review A, 2011

We present results on coherent control of ultracold trap-loss collisions using 40 ns pulses of no... more We present results on coherent control of ultracold trap-loss collisions using 40 ns pulses of nonlinearly frequency-chirped light. The chirps, either positive or negative, sweep ∼ 1 GHz in 100 ns and are centered at various detunings below the D2 line of 85 Rb. At each center detuning, we compare the collisional rate constant β for chirps that are linear in time, concave-down and concave-up. For positive chirps, we find that β generally depends very little on the shape of the chirp. For negative chirps, however, we find that β can be enhanced by up to 50(20)% for the case of the concave-down shape. This occurs at detunings where the evolution of the wavepacket is expected to be coherent. An enhancement at these detunings is also seen in quantum mechanical simulations of the collisional process.

A description of photoassociation by CW laser is formulated in the framework of grid methods. The... more A description of photoassociation by CW laser is formulated in the framework of grid methods. The Hamiltonian describing one or several bound states coupled to a multiple of continuum manifolds via a radiative field is written in the energy representation and diagonalized. The generality of the treatment allows to compute accurately and efficiently physical properties such as non-linear high-intensity energy shifts, line shapes, and photoassociation rates both for isolated and non-isolated resonances. Application is given to sodium photoassociation in the experimental conditions of Mc Kenzie et al [Phys. Rev. Lett. 88, 090403 (2002)]. Inverted region for the dependency of the rate vs. the intensity and non-symmetric lineshapes were predicted to occur above the saturation limit. Comparison with the model of Bohn and Julienne [Phys. Rev. A 60, 414 (1999)] is discussed. PACS numbers:

ABSTRACT We report on the results of quantum calculations of ^87Rb2 formation from ultracold atom... more ABSTRACT We report on the results of quantum calculations of ^87Rb2 formation from ultracold atoms by pulses of frequency-chirped light on the nanosecond timescale. This time-dependent photoassociation is modeled by following the dynamics of the collisional wave functions on both ground-state and excited-state potentials in the presence of the chirped light. Because of the relatively long time scales involved, spontaneous emission from the excited state must be accounted for. Results of the calculations are compared to recent measurements made with 40 ns FWHM Gaussian pulses and chirps that sweep 1 GHz in 100 ns. Dependencies on pulse intensity and chirp direction will be presented. This work is supported by DOE.

Physical Review A, 2007

We demonstrate the ability to coherently control ultracold atomic Rb collisions using frequency-c... more We demonstrate the ability to coherently control ultracold atomic Rb collisions using frequency-chirped light on the nanosecond time scale. For certain center frequencies of the chirp, the rate of inelastic trap-loss collisions induced by negatively chirped light is dramatically suppressed compared to the case of a positive chirp. We attribute this to a fundamental asymmetry in the system: an excited wave packet moves inward on the attractive molecular potential. For a positive chirp, the resonance condition moves outward in time, while for a negative chirp, it moves inward, in the same direction as the excited wave packet; this allows multiple interactions between the wave packet and the light, enabling the wave packet to be returned coherently to the ground state. Classical and quantum calculations support this interpretation.

Physical Review A, 2011

The major task in quantum control theory is to find an external field that transforms the system ... more The major task in quantum control theory is to find an external field that transforms the system from one state to another or executes a predetermined unitary transformation. We investigate the difficulty of computing the control field as the size of the Hilbert space is increased. In the models studied the controls form a small closed subalgebra of operators. Complete controllability is obtained by the commutators of the controls with the stationary Hamiltonian. We investigate the scaling of the computation effort required to converge a solution for the quantum control task with respect to the size of the Hilbert space. The models studied include the double-well Bose Hubbard model with the SU(2) control subalgebra and the Morse oscillator with the Heisenberg-Weil algebra. We find that for initial and target states that are classified as generalized coherent states (GCSs) of the control subalgebra the control field is easily found independent of the size of the Hilbert space. For such problems, a control field generated for a small system can serve as a pilot for finding the field for larger systems. Attempting to employ pilot fields that generate superpositions of GCSs or cat states failed. No relation was found between control solutions of different Hilbert space sizes. In addition the task of finding such a field scales unfavorably with Hilbert space sizes. We demonstrate the use of symmetry to obtain quantum transitions between states without phase information. Implications to quantum computing are discussed. 10 J = 5 J = 10 J = 20 J = 40 J = 80 J = 160 J = 320

Chemical Physics Letters, 2006

The origin of an artifact known as the appearance of ghost states in mapped Fourier grid methods ... more The origin of an artifact known as the appearance of ghost states in mapped Fourier grid methods is investigated. It was found that the ghost states can be attributed to under sampling of the high momentum components which are folded from the inner to the outer region of the potential to create the ghosts. The effect was corrected by addition of a complex potential at the outer region. The exterior complex potential was shown to shift the ghost states to the continuum part of the spectrum in a controllable way. The various methods to improve the mapped grid method are discussed in this context, and the use of zero boundary conditions is shown to be not essential.

Physical Review A - Atomic, Molecular, and Optical Physics, 2008

Bound-state molecules can be photoassociated directly from ultracold free-atom pairs by excitatio... more Bound-state molecules can be photoassociated directly from ultracold free-atom pairs by excitation to a purely repulsive electronic state. The process is explained on the basis of quantum unitarity: the initially free-scattering state is transformed by an impulsive light pulse to a deformed superposition which contains bound-state components. For pulse durations which are short compared to the ultracold dynamics, the maximal rate of photoassociation was found to be determined by the initial stationary distribution of scattering states of the atom pairs. The process was simulated for an ultracold gas of Rb with a temperature of T=44 K and a density of 10¹¹ cm³. Transform-limited pulses maximize the photoassociation, yielding 1 bound molecule per pulse. Coherent control calculated by a local control scheme can increase the photoassociation yield by two orders of magnitude.

Physical Review A, 2013

We use frequency-chirped light on the nanosecond time scale to produce ultracold 87 Rb2 molecules... more We use frequency-chirped light on the nanosecond time scale to produce ultracold 87 Rb2 molecules in the lowest triplet state via the process of photoassociation. Comparing to quantum simulations of the molecular formation, we conclude that coherent stimulated emission plays an important role and is primarily responsible for the significant difference observed between positive and negative chirps.

Physical Review A, 2012

Quantum control tasks are classified either as classical-like or as quantum requiring interferenc... more Quantum control tasks are classified either as classical-like or as quantum requiring interference of pathways. We study the generation of interference pathways and relate them to the fidelity of the control target at a fixed time for various tasks. The model drift Hamiltonian studied is the two-dimensional Henon-Heiles (HH) potential. This system shows regular classical dynamics for low energies and chaotic dynamics for higher energies. A control operator supported by the whole momentum space and therefore connecting the entire Hilbert phase space is a random spiky potential. The other extreme is a smooth control potential. Intermediate cases are obtained by filtering the random spiky potential in momentum space. The fidelity of achieving a control task was related to the connectivity in phase space of the control operators. Typical quantum tasks such as generating a superposition of generalized coherent states rely on interfering pathways. For these cases the nonlinearity in the drift or control Hamiltonian is a necessary requirement for creating interferences. Control over rapidly diverging components of the wave function is achieved by the use of highly nonlocal control operators. Quantum control under chaotic drift was found to give a better yield than control under regular dynamics for such cases. For classical tasks we study the transformation of an initial generalized coherent state to another one. The best fidelity is obtained for regular or harmonic regions of the potential and smooth control operators. The approach to the classical limit is checked by decreasing the effective value ofh. Control under both quantum and classical tasks suffered from the decrease ofh and the approach to classical proximity. Classical control tasks which rely heavily on maintaining a generalized coherent state throughout the evolution were found to be dysfunctional and lead to a completely uncontrolled situation once the classical chaos starts to appear.

Physical Review A, 2006

The problem of automatically protecting a quantum system against noise in a closed circuit is ana... more The problem of automatically protecting a quantum system against noise in a closed circuit is analyzed. A general scheme is developed built from two steps. At first, a distillation step is induced in which undesired components are removed to another degree of freedom of the system. Later a recovering step is employed which the system gains back its initial density. An Optimal-Control method is used to generate the distilling operator. The scheme is demonstrated by a simulation of a two level byte influenced by white noise. Undesired deviations from the target were shown to be reduced by at least two orders of magnitude on average. The relations between the quantum version of the classical Watt's Governor and the field of quantum information are also discussed.

Physical Chemistry Chemical Physics, 2010

The well-documented propensity of negatively-chirped pulses to enhance resonant impulsive Raman s... more The well-documented propensity of negatively-chirped pulses to enhance resonant impulsive Raman scattering has been rationalized in terms of a one pulse pump-dump sequence which &amp;amp;amp;amp;amp;amp;amp;amp;quot;follows&amp;amp;amp;amp;amp;amp;amp;amp;quot; the evolution of the excited molecules and dumps them back at highly displaced configurations. The aim of this study was to extend the understanding of this effect to molecules with many displaced vibrational modes in the presence of condensed surroundings. In particular, to define an optimally chirped pulse, to investigate what exactly it &amp;amp;amp;amp;amp;amp;amp;amp;quot;follows&amp;amp;amp;amp;amp;amp;amp;amp;quot; and to discover how this depends on the molecule under study. To this end, linear chirp effects on vibrational coherences in poly-atomics are investigated experimentally and theoretically. Chirped pump-impulsive probe experiments are reported for Sulforhodamine-B (&amp;amp;amp;amp;amp;amp;amp;amp;quot;Kiton Red&amp;amp;amp;amp;amp;amp;amp;amp;quot;), Betaine-30 and Oxazine-1 in ethanol solutions with &amp;amp;amp;amp;amp;amp;amp;amp;lt;10 fs resolution. Numerical simulations, including numerous displaced modes and electronic dephasing, are conducted to reproduce experimental results. Through semi-quantitative reproduction of experimental results in all three systems we show that the effect of group velocity dispersion (GVD) on the buildup of ground state wave-packets depends on the pulse spectrum, on the displacements of vibrational modes upon excitation, on the detuning of the excitation pulses from resonance, and on electronic dephasing rates. Akin to scenarios described for frequency-domain resonance Raman, within the small-displacement regime each mode responds to excitation chirp independently and the optimal GVD is mode-specific. Highly-displaced modes entangle the dynamics of excitation in different modes, requiring a multi-dimensional description of the response. Rapid photochemistry and ultrafast electronic dephasing narrow the window of opportunity for coherent manipulations, leading to a reduced and similar optimal chirp for different modes. Finally, non-intuitive coherent aspects of chirp &amp;amp;amp;amp;amp;amp;amp;amp;quot;following&amp;amp;amp;amp;amp;amp;amp;amp;quot; are predicted in the small-displacement and slow-dephasing regime, which remain to be observed in experiment.

Chemical Physics Letters, 2004

A fully-selective population transfer scheme for diatomic molecules using short-duration (<ns) la... more A fully-selective population transfer scheme for diatomic molecules using short-duration (<ns) laser pulses is developed via the concept of light-induced potentials. It explicitly takes rotational degrees of freedom into account. We apply it to a specific Na 2 transition from the lowest ro-vibrationic state to a single ro-vibrational state of a doubly excited electronic state via an intermediate electronic state. The process insures total selective population transfer with pulses short compared to the molecule rotation time. However, an estimate of the multiphoton ionization rate using time-dependent density functional theory suggests that ionization may significantly adversely affect the transfer.

Quantum control with noisy fields: computational complexity vs. sensitivity to noise Abstract. A ... more Quantum control with noisy fields: computational complexity vs. sensitivity to noise Abstract. A closed quantum system is defined as completely controllable if an arbitrary unitary transformation can be executed using the available controls. In practice, control fields are a source of unavoidable noise, which has to be suppressed to retain controllability. Can one design control fields such that the effect of noise is negligible on the time-scale of the transformation? This question is intimately related to the fundamental problem of a connection between the computational complexity of the control problem and the sensitivity of the controlled system to noise. The present study considers a paradigm of control, where the Lie-algebraic structure of the control Hamiltonian is fixed, while the size of the system increases with the dimension of the Hilbert space representation of the algebra. We find two types of control tasks, easy and hard. Easy tasks are characterized by a small variance of the evolving state with respect to the operators of the control operators. They are relatively immune to noise and the control field is easy to find. Hard tasks have a large variance, are sensitive to noise and the control field is hard to find. The influence of noise increases with the size of the system, which is measured by the scaling factor N of the largest weight of the representation. For fixed time and control field as O(N ) for easy tasks and as O(N 2 ) for hard tasks. As a consequence, even in the most favorable estimate, for large quantum systems, generic noise in the controls dominates for a typical class of target transformations, i.e., complete controllability is destroyed by noise.