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Progress in Quantum ElectromechanicsContinuous

Position Detection Near the Quantum Limit

- Keith Schwab, Laboratory for Physical Sciences
- National Security Agency
- August 2004
- schwab_at_lps.umd.edu

This work is supported entirely by NSA

My Group and Collaborators

Laboratory for Physical Sciences (LPS) Marc

Manheimer NSA Carlos Sanchez UMCP-grad

student Akshay Niak UMCP-grad student Ben

Palmer NSA Elinor Irish Rochester-grad

student Olivier Buu post doc Matt LaHaye

UMCP-grad student Patrick Truitt UMCP-grad

student Benedetta Camarota post doc Alex

Hutchinson post doc Harish Bhaskaran UMCP-grad

student Dan Stick Univ. Michagan-grad

Cooper-Pair Box

Nanomechanics

Atomic Traps

Collaborators Michael Roukes and his group

Caltech Chris Hammel and Denis Pelekhov Ohio

State Miles Blencowe Dartmouth Andrew Armour

Nottingham Asa Hopkins, Kurt Jacobs, and Salman

Habib LANL Ivar Martin LANL Halina

Rubinsztein-Dunlop Univ. of Queensland Chris

Monroe Univ. of Michigan Kamil Ekinci Boston

University Pierre Echternach JPL / Caltech

Examples of Nanomechanical Devices

Quantized Thermal Transport

MRFM detectors

Simple Nanomechanical Resonators

Integrated rf SET

Atomic Traps

Quantum limits of position detection

There are two pieces to this system which have

quantum limits Massive resonator Amplifier

k

M

Dx

For one instantaneous measurement no limit

detector

How close have other come?

2 Ton Acoustic Resonators-Auriga

Single-Spin Microscopes

4 km Interferometers - LIGO

SETNanomechanics

Energy Quantization - Freeze-Out

Oscillator occupation number T(mK) n(1kHz) n(10

MHz) n(100MHz) n(1GHz) 1000 2 107 2070 207 20

100 2 106 207 20.7 1.6 10 2 105

20.8 1.6 0.008 1 2 104 1.6 0.008 10-21 0.

50 1 104 0.6

SET Position Measurement

Energy sensitivity of rf SET has been

demonstrated to be 4.8 ? (not including back

action) Assime APL 2001.

Coupling

J

J

island

Blencowe and Wybourne, APL 77, 3845 (2000)

SET IVs and Modulation

Fix VG, measure IDS vs VDS

Fix VDS, measure IDS vs VG

Conductance of SET is depends upon applied charge

Back-action from SET

Physical Circuit

Noise in Electrical Circuits

Electro-Mechanical Circuit

Vds

Vn

G

e

In

Z

Sff

Cg(x)

e

Cj

SI

G

Vg

IDS

Korotkov, PRB (1994).

Complete Noise Model

Read-out noise due to shot noise

SET island

SQ

G

SV

Cm

Cg

2CJ

Back action voltage fluctuations

Lm

RJ

Rm

SThermal

Mechanical Resonator

Displacement Resolution at the Sweet Spot

Quantum Back action

RF SET coupled to Nanomechanics

L

C

SETmechanics on SiN membrane

RF SET coupled to Nanomechanics

RF SET coupled to Nanomechanics

gate

20 MHz resonator

SET

Recent Devices-RF SET coupled to Nanomechanics

200nm

Au

100 nm SiN

Cryogenic and electronicsetup

(No Transcript)

(No Transcript)

Resonance Detection with rf SET

Vdrive

VG

mwave reflectometry

Mechanical resonance detected by

electrostatically driving beam.

Thermal Motion of Nanomechanics

Equipartion Theorem

Noise Temperature of our system with VG2V

Thermal Motion 5.4 10-13mRMS _at_ 500mK 2.4

10-13mRMS _at_ 100mK

Nanomechanical Noise Thermometry

Detection Noise Temperature

TN/TQ33

Dx/DxQL5.8

Measured Displacement Resolution

Quantum Back action

LaHaye, et al, Science, 2 April 2004

Nanomechancis at Freeze-Out

freeze-out to 1D phonon channels

Measurement of the quantum of thermal

conductance K. Schwab, E.A. Henriksen, J.M.

Worlock M.L. Roukes NATUREVOL 40427 APRIL 2000

Strong Coupling Experiments

Classical dynamics of a nanomechanical resonator

coupled to a single-electron transistor, A. D.

Armour, M. P. Blencowe, and Y. Zhang, Phys. Rev.

B 69, 125313 (2004)

Strong Coupling Experiments

Mechanical Mode

Phonon Bath

SSET

Classical dynamics of a nanomechanical resonator

coupled to a single-electron transistor, A. D.

Armour, M. P. Blencowe, and Y. Zhang, Phys. Rev.

B 69, 125313 (2004)

Q vs Temperature

Q reached 200,000 for low SET coupling voltages

Active Cooling to the Ground State

Feedback Cooling of a Nanomechanical Resonator

Jacobs, Hopkins, Habib, and Schwab, PRB 68,

235328 (2004). Quantum Squeezing through

Feedback, Korotkov and Schwab, in preparation

Calculations using a model of continuous quantum

measurement, includes all sources of quantum

noise (including quantum projection noise and

quantum amplifier noise) feedback cooling to

N1-0.1 is possible.

Feedback Cooling-Recent Experiments

Warming and Cooling

Feedback on

Feedback off

Thermodynamics of a single degree of freedom

Cooling in Phase Space

What can we do with QL continuous position

measurement?

- rf SSET coupled to a 20 MHz resonator
- search for higher order modes
- achieve freeze-out, deviation
- from classical equipartition
- N f l
- 1 20 MHz 8 mm
- 3 110 MHz 3.4 mm
- 5 270 MHz 2.1 mm
- 7 500 MHz 1.6 mm
- 9 800 MHz 1.3 mm
- rf SSET coupled to a 1 MHz resonator
- increase coupling by reducing gap,
- observe back action fluctuations
- (Armour and Blencowe, Martin and Mozyrsky )
- drive dc current through resonator
- observe mech. noise from impact of electrons
- (Shytov, et al. PRL 2002) TN100mK 1K

Back-Action Physics

Coupling to SET will cause a damping and

fluctuations

See A. Armour and M. Blencowe,

\condmat0307528 Mozyrsky and Martin, PRL 89,

018301 (2003). recent work of A. Clerk.

Mind the Gap

Resonator

100-75 nm Gap

Au Gate

Please make 4,000 samples

5mm chip

150 mm dia. Coil

1mm wide lines-photolithography

Samples fabricated by MEMS-Exchange

Coupling to Coherent Quantum Devices

Quantum Two Level System Nuclear Spin Electron

Spin Charge on Cooper-Pair Box Flux in a SQUID

ring ..

10-21 Nt . 10-18 Nt. 10-13

Nt.. 10-9 Nt..

Schrodingers Cat Situation Macroscopic state

depends on microscopic quantum state Schrodi

ngers Whisker

Armour, Blencowe, and Schwab, Phys. Rev. Lett.

88, 148301 (2002).

Coherence times of the mechanics

Lifetime for number state

Decoherence time for superposition of coherent

states

Zurek, Habib, Paz, PRL 70, 1187 (1993).

Quantum Electro-Mechanics

Mirror

Interaction is through capacitance

Armour, Blencowe, Schwab, PRL 88, 148301

(2001). Armour, Blencowe, Schwab, Physica B 316,

(2002). Irish and Schwab, PRB 68, 15531 (2003).

Energy Scales and Linewidths

100 MHz - 1 GHz linewidth 1 kHz - 1 MHz

Mechanical States

2-50 GHz linewidth 0.5 - 3 MHz

Charge States

Mechanical Cooling Through Laser Cooling of

Qubit?

Decay of charge state without change in

mechanical state

Ground State Cooling of mechanical resonators,

Martin, Shnirman, Tian, and P. ZollerPhys.

Rev. B 69, 125339 (2004)

Conclusions

- Closest approach to the Uncertainty Principle, lt

10 DxQL - Back action of SSET at 20 MHz is near ideal
- Back action at 50 GHz is terrible! (CPB

experiments) - Observed resonator cooled to N 58 hw
- Starting feedback cooling thermal relaxation of

single mode - Entanglement with solid state qubits looks

possible mechanical superpositions - Nanomechanical QED experiments look promising
- Are mechanical resonators useful as a quantum bus

for charge qubits?

This work is supported by National Security

Agency (NSA) Our Motto Putting the Spook in the

Spooky actions at a distance

schwab_at_lps.umd.edu

Calculated Dynamics

Initial state

Intermediate state

Probability Density

After one period

1.10-13 m

Cavity Quantum Electro-Dynamics

Mirror

Atom

Mode

Cavity QED analog QEM

Quantum Electro-Mechanics

Quantum Electro-Dynamics

Armour, Blencowe, Schwab, PRL 88, 148301

(2001). Armour, Blencowe, Schwab, Physica B 316,

(2002). Irish and Schwab, PRB 68, 15531 (2003).

Second Order Shift of Energy Levels

Treat HI as a perturbation

Quantum Measurement with a coupled

Nanomechanical ResonatorCooper Pair Box System,

E. Irish and K. Schwab, Phys. Rev. B 68, 155311

(2003)

Mechanical Dressed States

Hamiltonian

Ignoring HI we find the unperturbed energy

Nanomechanical Quantum Bus

For a 1 mm wide Diamond beam (E1000GPa) 1 GHz l

6 mm 10 GHz l 2 mm For a 1 mm wide Silicon

beam (E110GPa) 1 GHz l 3.5 mm 10 GHz l

1.2 mm

What is the Q of these higher order modes? What

is the effect of the other modes? Possible

source of decoherence? Advanced materials

Piezoelectric or nanotubes?

Coupling strength

Penrose Proposal

Low photon pressure requires very soft cantilever

(even after amplify dwell time with cavity) Very

soft cantilever has very low frequency

1KHz Low frequency cantilever has very low

freezeout temperature 60mK

Support

C60fF

L150nH

BOX

2e-charge states Good!

SET Gate

1µm

quasi-particle poisoning Bad!

SET

Spectroscopy of Box

Coherent oscillations

?t

- Send pulses continuously
- Measure staircase with SET

Tr500ns

Coherent Single ElectronicsCooper-Pair Box

Ultra-small capacitance (lt10-15 F)

--------- charge eigenstates Superconducting

--------- follows Josephson equations of

motion

Cooper Pair Binding energy D230mV Charging

energy Ec e2/2C 100mV Josephson energy EJ

50-10mV Thermal energy T 3mV (30 mK) D

gt Ec gtEJ gtkBT

Energy Spectrum of Cooper-Pair Box

At level crossing, states are superposition of

charge states.

DE50-1 GHz Decoherence time measured to be

t20.5msec And excited state lifetime of

t12msec. Vion, et al, Nature 2002.

Coherence time of position-superposition states

Decoherence time

Typical resonator decay time Number of Coherent

Oscillations For 100 MHz at 10 mK.

Zurek, Habib, Paz, PRL 70, 1187 (1993).

Who is interested in Quantum Limits of motion?

Gravitational Wave Detectors

Interferometers-LIGO

Mechanical Resonators-Auriga

Looking for displacements on the order of

Dl/l10-21 Quantum Limits of the Mega-world.

Temperatures?

Clearly the thermal bath which determines f and Q

is different than the mode temperature.

Charge States Coulomb Staircase

Measure response at SET

Sweep Box gate Voltage

Reality Check A typical fabrication result!

Shift of the CPB by Resonator Fock States

Mechanical Lamb shift Mechanical Lamb-shift

analogue for the Cooper-pair box, A.D. Armour,

M.P. Blencowe, and K.C. Schwab,

By driving transitions in the Box, one should be

able to prepare a mechanical number

state perform QND measurement of number using

Ramsey interferometry (Vion, 2002)

Shift of the Resonator frequency by the CPB

wm300MHz, l0.1hwm, EJ4mV, EC100mV

By measuring the mechanical frequency we can know

the state of the phase states of the box.

Quantum Phenomena in Mechanical Structures

First kind Uncertainty Principle-Limited

Detection

Second kind Energy Level Quantization

Third kind Superpositions and Coherent

Evolution

Fourth kind Controlled Entanglement with

other quantum systems

What is Quantum Electro-Mechanics?

- Single Electron Transistors
- Cooper-Pair Box
- Quantum Dots
- Quantum Point Contacts
- SQUIDs
- Single electron spins
- ..

kBThn just a few quanta tDgt 1/n long

coherence times

Exploit the quantum electronics to both detect

and generate the quantum nature of the mechanical

device.

Magnetomotive Readout of Nanomechanics

R

TN

B

Sensitivity of Magnetomotive? Not

very! TN30K

Fabrication by LaHaye and Hutchinson

Back action of the SSET onto the CPB

Back-action from phonons or photons emitted when

quasi particles in SET recombine?

Can we engineer D?

Can we detect the Thermal Motion?

Amorphous Silicon Nitride resonator

Conditions f0 23MHz Q 104 T

4.2K B9T Thermomechanical Noise xRMS 2 pmRMS

gt 8 nVRMS XRMS (4.2K) 1.4 pm 60 XSQL

To approach quantum limits motion we need a

quantum limited linear amplifier SQUIDs and SETs

Displacement Resolution Sweet Spot

Quantum Back action

Shot Noise

Back Action Noise

Recent Devices-RF SET coupled to Nanomechanics

1 mm

SET island

junctions

Mechanical Entanglement

Idea Use the superposition available in a

Cooper-pair box to place a mechanical system in a

superposition For two different charge states of

the box, the position of the resonator can change

by as much as 12pm gt xSQL100fm

What will the effect of the mechanical mode on

the Cooper-pair box? How long will a

superposition survive? Armour, Blencowe, and

Schwab, Phys. Rev. Lett. 88, 148301 (2002).

Can we make the resonator interfere with itself?

You Bet!, send a p/2 pulse to the box after the

systems have entangled This produces states like

Interference terms

By measuring Box, we can create mechanical

superposition states

Probability Density

1.10-13 m

Decoherence and Recoherence

Envelope on Ramsey interference experiment

should reveal entanglement with mechanics

Armour, Blencowe, and Schwab, PRL 88, 148301

(2002).

Mixed state

Total State

Expectation Value

What can we learn?

- This teaches us how to engineer quantum limited

detection where hw is growing smaller and smaller

(attempt at MHz) on systems that have huge

numbers of degrees of freedom that must be

controlled. - This forces us to consider carefully the

interaction between the measuring device and the

measured quantum system. These studies will

teach us intelligent measurement strategies (QND,

indirect measurement, stroboscopic..) (Quantum

Engineering) - Reveals the physics of decoherence and

entanglements, relevant to the engineering of

quantum coherent solid state devices (Quantum

Computers?) - This work will push the boundary between the

classical world that we live in and the bizarre

behavior that underlies reality (Foundations of

Physics).

Will Quantum Mechanics break-down on large length

scales?

Ramsey Interference Experiments

Interaction Region

State Measurement

p/2 pulse

p/2 pulse

State Preparation

Space or Time

Traps for BEC Univ. of Queensland

Fabricated by Ashley Carter

13 mm thick Al film

30 mm wide etched gap

15-30 mm wide wires

Microfabricated Ion Traps Univ. of Michigan

Top view

First etch into GaAs

10mm

View behind chip

Fabricated by Dan Stick

RF -SET Nanomechanics

See Adrian Cho, Science 299, 36 (2003).

Can we exploit what is known from atomic physics?

Laser Cooling Atom in crossed laser field, red

tuned from transition

When atom moves, it encounters light on

resonance, absorbs photon and re-radiates this

into 4p. Kinetic Energy -gt Radiation into cold

reservoir

Nanomechanical Cooling Can we engineer a

situation where the motion of a nanomechanical

device leads to a force, pushing it back towards

equilibrium? By interaction with an SET, a

quantum dot, ect?

Frequency and Q Tuning Using an SET

What will happen if we place the SET island on

the nanomechanical resonator and place this

system in a large magnetic field? We can tune the

frequency and adjust the damping.. Schwab,

Appl. Phys. Lett. 80, 1276 (2002).

B

When SET moves, current changes resulting in a

change in the Lorentz force---- will add spring

constant When SET moves, voltage is developed

(Lenzs Law) resulting in a change in SET

current, resulting in a change in the Lorentz

force ----- will add damping constant

Lorentz Spring Constant

Losses Q modification

Plot for 10MHz Si resonator (7mm X 50nm X50nm)

Emf generated will give an additional damping

force to resonator, depending on VG.

The numbers..

Table I silicon (Si), single wall nanotubes

(SWNT), nanotube bundles (B-SWNT), with length l,

width w, thickness t, mass m, resonant frequency

wo, mechanical spring constant kM, maximum bias

voltage VMAX, Lorentz spring constant kL, range

of frequency tuning Dwo/wo, and least upper bound

on quality factor QL, For the nanotube

resonators, it is assumed that the density is

1100 Kg/m3, Youngs modulus 1000 GPa, CG10 aF,

CJ10 aF.

Suggestions to approach quantum limits

- Must incorporate detection with mechanical device

to overcome ultra(high/low) output impedance of

nanomechanics-detection schemes with noise

temperature TNlt1K - High frequencies gt100MHz
- to avoid 1/f or similar noise in detector or

background forces - to approach thermal freeze-out to ground state
- to have long decoherence times
- Stiff-low density materials Diamond and Silicon

Carbide - need to routinely approach 1GHz- couple well to

qubit energies - Integrate magnetic materials for force

sensing-Magnetic microscopy - Exploit recent developments in solid state

Quantum Computing coherent electronic devices - Engage theorist to guide these experiments and to

produce measurement strategies (squeezing,

entanglement, non-classical state formation.)

Questions

- Can we generate an approximation to an arbitrary

wave function of resonator by coherent control of

two level system (CPB)? - Can we exploit this for metrology? Single spin

detection? Weak force detection beyond Standard

Quantum Limit? - Can we test Quantum Mechanics, (and how do we

distinguish new physics from bad experimental

technique?)

Why is there no interference?

System state

Incoherent Sum of Probability Distributions

Physics of decoherence by entanglement with

environment.

Control of the Wavefunctions

Uncoupled systems

Coupled and Entangled systems

Signature of the Entanglement

Expect to see a modulation on the coherent

oscillations of the Cooper-Pair box at the

resonator frequency (N.B. no fancy detectors

needed to monitor the mechanical resonator.)

Nanomechanical resonator is an engineered

environment Similar to other proposed schemes

with electro-magnetic resonators Marquardt and

Bruder, Phys. Rev. B, vol. 63, 054514-1

(2001) Buisson and Hekking, cond-mat/0008275

Some References on SETs

SET Single Charge Tunnelling, edited by Devoret

and H. Grabert, (Plenum, New York,

1992). Single-electron transfer in metallic

nanostructures, M. Devoret, et al., Nature 360,

547 (1992). Instrinsic Noise of a single

electron transistor, A. Korotkov, Phys. Rev. B

49, 10381 (1994). Charge sensitivity of a single

electron transistor, U. Hanke, et al., Appl.

Phys. Lett. 65, 1847 (1994). Charge sensitivity

of superconducting single-electron transistor,

A. Korotkov, Appl. Phys. Lett. 69, 2593

(1996). Take a look at more references from

Korotkov for calculations of fluctuations and

sensitivity of SETs. Quantum-Limited

Electrometer based on Single Cooper-Pair

tunneling, A. Zorin, Phys. Rev. Lett. 76, 4408

(1996). Highly sensitive electrometer based on

single cooper pair tunneling, A. B. Zorin, et

al., J. Appl. Supercon 12, 747 (1999). This is

a more advanced SET which looks sort-of-like an

electrostatic SQUID. The most interesting

feature is that the tunneling is coherent

Josephson tunneling which produces a sinusoidal

back-action (as opposed to the white noise

spectrum of the backaction in a normal SET.

) The radio frequency single electron transistor

(RF-SET)a fast and ultrasensitive electrometer,

Science 280, 1238 (1998). Amplifying quantum

signal with the single electron transistor, M.

Devoret and R. Schoelkopf, Science 19, 19

(2000). Radio Frequency single-electron

transistor, P. Wahlgreen, el al., J. Supercond.

12, 741 (1999). Radio-frequency single-electron

transistor Toward the shot-noise limit, A.

Aassime, et al., Appl. Phys. Lett. 79, 4031

(2001). SET and nanomechanics Sensitivity of a

micromechanical displacement sensor based on the

radio-frequency single electron transistor, M.

Blencowe and M. Wybourne, Appl. Phys. Lett. 77,

3845 (2000). They did not include the SET

backaction onto the nanomechanical

resonator. Intrinsic noise of a micromechanical

displacement detector based on the

radio-frequency single-electron transistor,Yong

Zhang and Miles P. Blencowe, J. Appl. Phys. 91,

4249 (2002). Quantum Measurement with

Nanomechanical Systems, K. Schwab, submitted to

the International Conference on Solid State

Implementations of Quantum Computing, Sydney,

Australia, January 2001. Here I estimatedthe back

action from the SET. A nanometre-scale

mechanical electrometer, A.N. Cleland, M.L.

Roukes, Nature 392, 160 (1998).

References

Quantum Effects in Mechanical Measurement Quantum

Measurement,Braginsky and Khalili, Cambride

University Press, 1992. On the detection of a

weak classical force coupled to a

quantum-mechanical oscillator. I. Issues of

principle, Caves, et al., Rev. Mod. Phys. 52,

341 (1980). Quantum Non-Demolition measurements

the route from toys to tools, V.B. Braginsky and

F. Ya. Khalili, Rev. Mod. Phys. 68, 1 (1996). On

the measurement of a weak classical force coupled

to a harmonic oscillator M. Boco and Roberto

Onofrio, Rev. Mod. Phys. 68, 755

(1996). Scheme to probe the decoherence of a

macroscopic object, S. Bose, K. Jacobs, and P.

Knight, Phys. Rev. A 59, 3204 (1999). Quantum

squeezing of mechanical motion for micron-sized

cantilevers, M.P. Blencowe, M. Wybourne, Physica

B 280, 555 (2000). Schroedinger Cat

formation.. G. Berman, xxx.lanl.gov Mechanical

Lamb-shift analogue for the Cooper-pair box,

A.D. Armour, M.P. Blencowe, and K.C. Schwab, to

appear in Physica B from the proceedings of

Phonons 2001, held at Dartmouth. The noise in

gravitational-wave detectors and other

classical-force measurements is not influenced by

test-mass quantization, V.B. Braginsky, et al.,

xxx.lanl.gov, gr-qc/0109003 Dynamics of damped

cantilever, S. Rast, et al., Rev. Sci. Inst. 71,

2772 (2000). Quantized Thermal Transport-Freeze

Out to 1D D.E. Angelescu, M.C. Cross, and M.L.

Roukes, Superlattices and Microstructures 23,

(1998). Luis G.C. Rego and George Kirczenow,

Phys. Rev. Lett. 81, 232 (1998). Miles Blencowe,

Phys. Rev. B 59, 4992 (1999). Measurement of the

quantum of thermal conductance, K. Schwab, E.A.

Henriksen, J.M. Worlock M.L. Roukes, Nature

404, (2000). Thermal conductance through

discrete quantum channels, K. Schwab, W. Fon,

E.A. Henriksen, J.M. Worlock, M.L. Roukes,

Physica E 9, 60-68 (2001). Elastic wave

transmission at an abrubt junction in a thin

plate with the application to heat transport and

vibrations in mesoscopic systems, M.C. Cross and

Ron Lifshitz, Phys. Rev. B 64, 085324

(2001). Thermal conductance of nanostructured

phononic crystals, A.N. Cleland, D.R. Schmidt,

C.S. Yung, Phys. Rev. B 64, 172301

(2001). Yactocalorimetry phonon counting in

nanostructures, M.L. Roukes, Physica B 263, 1

(1999). by interaction with a Cooper pair box.

More References.

Cooper-Pair Box and Entanglement with Resonators

of various kinds Quantum Dynamics of a

Cooper-Pair Box Coupled to a Micromechanical

Resonator, A.D. Armour, M.P. Blencowe, and K.

Schwab, Phys. Rev. Lett. 88, 148301 (2002).

Coherent control of macroscopic quantum states

in a single-Cooper-pair box Y. Nakamura, et al.,

Nature 398, 786 (1999) Quantum state engineering

with Josephson-junction devices,

cond-mat/0011269, Yuriy Makhlin, Gerd Schoen,

Alexander Shnirman This reference is really an

excellent description of the cooper-pair

qubit. Superposition of two mesoscopically

distinct quantum states Coupling a Cooper-pair

box to a large superconducting island, F.

Marquardt and C. Bruder, Phys. Rev. B 63, 054514

(2001). Buisson and Hekking, cond-mat/0008275

Single electronics and Nanomechanics

100 nm SiN membrane

50 nm Au

Fabrication by Matt LaHaye and Alex Hutchinson

Tunnel Junctions and SET island

50 nm Al

How cold will they get?

Nano-electronic devices rarely ever get below

30mK due to the very weak coupling between

electrons and phonons. (See Roukes, et al., PRL,

(1985).)

Celect

Where W is the volume and S is the

electron-phonon coupling 2 109 W/m3/K5 for

Au. For example it will only take 10-15 W to

hold a 1mm3 of Au at 50mK with phonons at

T0. However, for a mechanical (phonon) device,

the connection to the bath is much stronger..

Coupled by 4 Sch-Roukes!

Thermal Circuit

Confidence in this estimate High See Matter

and Methods of Low Temperatures, Pobell

Confidence in this estimate High See Schwab, et

al. Nature, 404, (2000).

Thermal situation for metal on top of mechanical

resonator.

Confidence in this estimate probably totally

wrong (Re-p should diverge as dimensionality is

reduced. ldomgtl,w,h). See Roukes, PRL (1985).

Experimental Limits to Electrical and Mechanical

Noise Temperatures

Mechanical noise temperature of a 290nm thick,

3.9 mm wide, 260 mm long cantilever, no5kHz,

Q150,000. Notice saturation in TN at 100mK --

could be fm/hz1/2 vibrations limiting noise

temperature. (should not be a problem for MHz

resonators)

Electrical noise temperature of a 30nm thick, 2

mm wide, 4 mm long Au resistor. Measured with

ultra-low power dc SQUID setup and with extensive

filters to room temperature connections. Notice

saturation in noise temperature at 80mK.

Current best is TNlt30mK (J. Hanolka, et al.,

Caltech).

Mamin and Rugar, APL 79, 3358 (2001).

Schwab, et al, Physica E 9, 60 (2001).

Some Useful SET Approximations

Current through the SET, measured at Blockade

voltage VDSe/CS

Transfer function of SET

Spectral density of the current noise through the

SET (about half that of shot noise)

Spectral density of the SET island potential

fluctuations (this is where the back-action

comes from)

Both equations are for wltt, where tRJCS See

Korotkov, PRB (1994).

Single Electron Transistor

Criteria for operation Thermal for 50nm X

50nm junctions, C10-15 F, so T ltlt

1K Quantum For island to be in a well defined

number state dnltlt1 charging time, t

RtunnellingC from uncertainty, we know dE t gt

h rearranging we find,

SET Fabrication

- Pattern with electron microscope
- Evaporate Al island
- Oxidized Al to form barriers
- Evaporate leads to island
- Junctions are typically 50nm X 50nm 10-16

-10-15 F - Fulton and Dolan, PRL 59, 109 (1987).

Fancy SETs Josephson Electrometer

- Zorin, Phys. Rev. Lett. 76, 4408 (1996).
- Zorin, J. of Supercon. 12, 747 (1999).
- Work with device in superconducting state
- with Junction resistance RQ
- And the environment seen by the device
- Must be much lower than RQ
- Advantages
- Josephson tunneling is non-dissipative so island

heating is not a problems - Voltage oscillations on the island are coherent

and at the Josephson frequency - Deterministic
- Monochromatic
- Reduced amplitude of charge fluctuations
- Sensitivity can be equal to that of normal state

SET 1me/rtHz - Lower impedance can be easier to read-out with

high frequency electronics - Disadvantages
- Most carefully engineer junction resistance and

environment

Josephson Electrometer Backaction

Charge oscillations of the island are at the

Josephson frequency (As opposed to white noise

from normal state SET)

With amplitude of e/C

Low frequency voltage oscillations of island from

Johnson noise of shunt

Improvement of factor of 20 over normal state SET.

Bottom line Total integrated noise power in both

cases is similar, difference is in spectral

distribution. Does this mean that we will be

limited only by the uncertainty principle of the

resonator mass?

Can we engineer the backaction?

Measure Here

Since the backaction of a Josephson electrometer

is dominated by a harmonic component at the

Josephson frequency, can we tune this to hit an

anti-resonance of the resonator? Then we will be

limited only by the white floor which is much

smaller. Can we take advantage of the coherent

tunneling to achieve parametric amplification?

Coupling to only one quadrature component of the

mechanical oscillation? Will it electrometer

SQUEEZE the resonator? Is there any effect at

w0 from mixing when wmwJ?

wJ

Backaction here

Dynamics of damped cantilever, S. Rast, et al.,

Rev. Sci. Inst. 71, 2772 (2000).

First LPS Nanomechanics

Silicon Nitride beams with Au electrodes 200 nm X

150 nm X 15 mm -gt 5 MHz Fabrication by Matt LaHaye

Thermal Motion of Resonator

f0 23MHz Q 104 T 4.2K XRMS 1.4 pm 60

XSQL B9T VRMS/rtHz 250 pVRMS /rtHz

Magneto-motive Readout Amorphous Silicon Nitride

resonator 8mm X 200nm X 150nm

rf SET Performance

Reflection Spectrum vs Gate voltage

1 MHz, 0.1 eRMS signal to gate

Recently demonstrated rf SET technique Charge

sensitivity 70 me/rtHz Bandwidth 50

MHz Carlos Sanchez

rf SET at LPS

Microfabricated microwave resonators

SET IV curves T20mK

LC-resonance at 1.3 GHz. Carlos Sanchez, Matt

LaHaye

SET Fabrication

Al-AlO-Al Tunnel Junctions

Single Electron Transistor

Carlos Sanchez (UMCP)

Sketch of Noise Analysis

DC Response of SETs

I-V curves for different VG

Modulation I-VG

Cooper-Pair Box

Coplanar Waveguide

Control Lines

Nb Capacitor

25 Turn Nb Inductor

Cooper-Pair Box

Nanomechanical Resonators

200 nm X 100 nm x 16-6 mm 50 nm of Au on 100 nm

of SiN Resonance of 10-100 MHz Matt LaHaye and

Alex Hutchinson

Coherent Single ElectronicsCooper-Pair Box

Ultra-small capacitance (lt10-15 F)

--------- charge basis is good QM

description Superconducting --------- follows

Josephson equations of motion

Vg

Quantum Effects in Mechanics

What behavior is possible???

- Position Detection limited by the Uncertainty

Principle (Force detection) - Energy quantization and freeze-out to the quantum

ground state - Quantized energy and zero-point fluctuations

Fock states and Lamb shifts - Superposition and Entangled states

..it all seems possible!

Schwab Group at LPS

- Cooper-Pair Box Qubits
- Exploration of coherent two-level electronic

system qubit - - Single-shot readout
- Nanomechanics
- rf SET position detection-approaching the

Standard Quantum Limit - Mesoscopic fluctuations with nano-mechanical

detection - Coupling to Cooper-Pair Box-superpositions and

coherent effects - Diamond NEMS (NRL and Cornell)
- Ultra-sensitive cantilevers for MRFM (Ohio

State-Caltech) - Nanofabrication for Atomic Physics
- Surface traps for BEC (Univ. of Queensland)
- GaAs devices for ion traps (Monroe-Univ. of

Michigan) - Ultra-sensitive Superfluid gyroscopes

(NASA/Goddard) - Using rf SET and nanostructures to read-out

superfluid SQUIDs - Understanding limits of superfluid rotation

detection

Mechanics and detection at the Quantum Limit

The Fundamental Quantum Condition

Uncertainty Principle leads to Standard quantum

limit for simple harmonic oscillator

See Braginsky, Khalili, Thorne, Quantum

Measurement

See Heffner, Proc. IRE 50, 1604

(1962). Giffard, Phys. Rev. D 14, 2478 (1976).

For continuous measurement including amplifier

back action

See C. Caves, et al., RMP 1982

Time Domain Experiments

T1.2K

104 cycles

digital scope

Free decay

TN

B

pulser

R

RF -SET Nanomechanics

100 mm

Recent Devices-RF SET coupled to Nanomechanics

Nanomechanics at the Quantum Limit

DilutionDemag Fridge

3He Fridge

Dilution Fridge

What refrigeration technology is necessary to get

to freezeout?

Freeze-out

Standard Quantum Limit

Measure average position of particle by two

consecutive measurements.

M

Before first measurement

After first measurement

Before second measurement

which minimizes when

Quantum Limit for Linear Amplifier

Ideal Detector

Linear Amplifier

See Heffner, Proc. IRE 50, 1604

(1962). Giffard, Phys. Rev. D 14, 2478 (1976). C.

Caves, et al., RMP 1982

Nanomechanical Noise Thermometry

Saturation does not seem to be from SET, but from

some other thermal source.

Recent SET results

VG

VDS

IDS

Mechanical detection of two-level systems

Forces are at the 10-18-10-21 Nt range

Scanned Magnetic Resonance Tool

F

Resonant Spins

Cantilever with magnet

Experiments of Rugar and Mamin and Hammel,

Pelekov, and Roukes

Quantum Limits of the Micro-world following the

dynamics of single engineered quantum systems

RFSET

- Operating frequency 1.5GHz
- Bandwidth 30MHz
- Sensitivity 8x 10-6 e/(Hz)1/2

staircase

- 1-e periodic at high Vds
- Quasi particle poisoned 2-e staircase at low Vds
- Worked with dc SET to avoid back action

Spectroscopy

?t

Tr

Refcond-mat/0305433, Duty et. al.

Summary

- Spectroscopy of the box
- Coherent oscillation in the box
- T1 350ns
- Future work
- Measure T2,T1
- Single shot measurement of charge states

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?t

Not for presentation

Tr

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CPB-rf SSET Experiments

CPB

F

CPB-Gate

SET-Gate

SET

Traps for BEC Univ. of Queensland

13mm thick Al carried 3A

Traps for Ions Univ. of Michigan

Epitaxial doped GaAs/AlGaAs

Sympathetic Cooling of Mechanical Mode

Rate at which quanta enter resonator from thermal

bath

Rate at which quanta are exchanged between

resonator and ion

Rate at which quanta are removed from ion

Quantum-limited cooling and detection of

radio-frequency oscillations by laser-cooled

ions, D. J. Heinzen and D. J. Wineland, Phys.

Rev. B 42, 2977 (1990).

from The Onion

Whats nano got to do with it?

t

l

Maximize E/r ? Diamond See Dissipation in

Nanocrystaline Diamond Nanomechanical

Resonators, Hutchinson, et al. APL, Feb. 2004.

Advanced Materials Diamond (NRL, Cornell, LPS)

E1TPa

Hutchinson, et al, APL 84, 972 (2004)

Back-action in an optical Interferometer

Fixed mirror

Pondermotive noise from radiation pressure

Shot noise of photon current

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Isolating the mechanics from dissipation in the

SET

.

Q

1 pW

Outline

- Intro and motivation
- Quantum limit of continuous position measurement
- Issues of principle
- Experimental approach - rf SSET coupled to a 20

MHz nanomechanical resonator - Our recent results
- Approach to within 4.3 of Uncertainty Principle
- Freeze-out to T 56 mK, NTH 58
- Beginning to Feedback cool 250mK -gt 70mK
- Future directions
- Feedback cooling to ground state and quantum

squeezing - Detection and freeze-out of higher order modes
- Resonator coupled to CPB Quantum

Electro-Mechanics

Improvements to fabrication

Use dry process to undercut no membrane Move

all photo lithography to foundry saves 4 layers

of litho

SiN

Au

Si

SET Primer

Ids

Vds

IDS

nCgVg/e

Superconducting SET

rf SET-Ideal Amplifier for Nanomechanics

Impedance of SET is monitored by measuring

microwave reflections Microwave tank transforms

50kW impedance to 50W

Charge sensitivity 5 m e/ rtHz Band

width 75 MHz 1/f knee 10,000 Hz

Schoelkopf, et al, Science 280, 1238

(1998). Wahlgreen, el al, J. Supercond. 12, 741

(1999).